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x^3+x=a (уравнение)

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     3        
x  + x = a
    $$x^{3} + x = a$$
    Быстрый ответ [src]
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       |       /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                                                       |          /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                                                       
       |      /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||               /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||                                                       |         /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||               /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||                                                       
       |     /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||              /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||                                                       |        /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||              /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||                                                       
       |    /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||             /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||                                                       |       /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||             /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||                                                       
       |   /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|     ___    /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|                                                       |      /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|     ___    /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|                                                       
       |6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   \/ 3 *6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                       |   6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   \/ 3 *6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                       
       |\/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /         \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /     /                       1                        \|   \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /         \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /     /                       1                        \
x1 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + im|------------------------------------------------|| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + re|------------------------------------------------|
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       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ||  1   I*\/ 3 |    /   \/  108 + 729*a     27*a ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               ||  1   I*\/ 3 |    /   \/  108 + 729*a     27*a |
       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ||- - - -------|*3 /    ----------------- - ---- ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               ||- - - -------|*3 /    ----------------- - ---- |
       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \\  2      2   / \/             2            2   //                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \\  2      2   / \/             2            2   /
    $$x_{1} = - \frac{\sqrt{3}}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \frac{1}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + i \left(\frac{1}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \frac{\sqrt{3}}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \Im{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 a}{2} + \frac{1}{2} \sqrt{729 a^{2} + 108}}}\right)}\right) + \Re{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 a}{2} + \frac{1}{2} \sqrt{729 a^{2} + 108}}}\right)}$$
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       |        /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||                 /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||                                                       |           /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||                 /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||                                                       
       |       /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                                                       |          /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||                                                       
       |      /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||               /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||                                                       |         /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||               /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||                                                       
       |     /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||              /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||                                                       |        /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||              /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||                                                       
       |    /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||             /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||                                                       |       /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||             /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||                                                       
       |   /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|     ___    /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|                                                       |      /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|     ___    /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|                                                       
       |6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   \/ 3 *6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                       |   6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   \/ 3 *6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|                                                       
       |\/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /         \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /     /                       1                        \|   \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /         \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /     /                       1                        \
x2 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + im|------------------------------------------------|| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + re|------------------------------------------------|
       |                                                                                                                                                                                                                                                                                               6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    6                                                                                                                                                                                                                                                                                                       |                      __________________________||                                                                                                                                                                                                                                                                                                  6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    6                                                                                                                                                                                                                                                                                                       |                      __________________________|
       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |                     /    ______________        ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |                     /    ______________        |
       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |/          ___\     /    /            2         ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |/          ___\     /    /            2         |
       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ||  1   I*\/ 3 |    /   \/  108 + 729*a     27*a ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               ||  1   I*\/ 3 |    /   \/  108 + 729*a     27*a |
       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ||- - + -------|*3 /    ----------------- - ---- ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               ||- - + -------|*3 /    ----------------- - ---- |
       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \\  2      2   / \/             2            2   //                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \\  2      2   / \/             2            2   /
    $$x_{2} = \frac{\sqrt{3}}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \frac{1}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + i \left(\frac{1}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} - \frac{\sqrt{3}}{6} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \Im{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 a}{2} + \frac{1}{2} \sqrt{729 a^{2} + 108}}}\right)}\right) + \Re{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 a}{2} + \frac{1}{2} \sqrt{729 a^{2} + 108}}}\right)}$$
           /        /     /                 __________________________________________________________                                                                               __________________________________________________________                                                            \\               _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________    /     /                 __________________________________________________________                                                                               __________________________________________________________                                                            \\\         /     /                 __________________________________________________________                                                                               __________________________________________________________                                                            \\               _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________    /     /                 __________________________________________________________                                                                               __________________________________________________________                                                            \\
       |        |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||              /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\|||         |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||              /                                                                                                                                          2                                                                                                                                            2     |     |                /                                2                             /     /                              2            2   \\                  /                                2                             /     /                              2            2   \\||
       |        |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||             /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||||         |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||             /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \      |     |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|               4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/|||
       |        |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||            /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||||         |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||            /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|      |     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------|               \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------|||
       |        |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||           /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /|||         |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||           /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||      |     |  27*im(a)                                                                     \                          2                           /    27*re(a)                                                                     \                          2                           /||
       |        |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||          /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------|||         |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||          /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||      |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------, - -------- + --------------------------------------------------------------------------------------------------------------------------||
       |        |     \     2                                                                   2                                                                    2                                                                   2                                                             /|         /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /||         |     \     2                                                                   2                                                                    2                                                                   2                                                             /|         /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|      |     \     2                                                                   2                                                                    2                                                                   2                                                             /|
       |     sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|      6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||      cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|      6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|  *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
       |        \                                                                                                                                           3                                                                                                                                           /      \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /|         \                                                                                                                                           3                                                                                                                                           /      \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /      \                                                                                                                                           3                                                                                                                                           /
x3 = I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |           _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                  3                                                                                                                                                                                                                                                                                               |            _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                  3                                                                                                                                                                                                                                                                                               
       |          /                                                                                                                                          2                                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |           /                                                                                                                                          2                                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
       |         /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |          /  /                 __________________________________________________________                                                            \    /                 __________________________________________________________                                                            \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       |        /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |         /   |                /                                2                             /     /                              2            2   \\|    |                /                                2                             /     /                              2            2   \\|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       |       /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |        /    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||    |             4 /  /            2            2   \              2      2        |atan2\1458*im(a)*re(a), 108 - 729*im (a) + 729*re (a)/||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       |      /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |       /     |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *sin|------------------------------------------------------||    |             \/   \108 - 729*im (a) + 729*re (a)/  + 2125764*im (a)*re (a) *cos|------------------------------------------------------||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       |     /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |      /      |  27*im(a)                                                                     \                          2                           /|    |  27*re(a)                                                                     \                          2                           /|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       |  6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |   6 /       |- -------- + --------------------------------------------------------------------------------------------------------------------------|  + |- -------- + --------------------------------------------------------------------------------------------------------------------------|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
       \  \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /   \/        \     2                                                                   2                                                             /    \     2                                                                   2                                                             /
    $$x_{3} = i \left(- \frac{1}{3} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} - \frac{\sin{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )}}{\sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}}}\right) - \frac{1}{3} \sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}} \cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )} + \frac{\cos{\left (\frac{1}{3} \operatorname{atan_{2}}{\left (\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2},\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2} \right )} \right )}}{\sqrt[6]{\left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \sin{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Im{a}}{2}\right)^{2} + \left(\frac{1}{2} \sqrt[4]{\left(729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108\right)^{2} + 2125764 \left(\Re{a}\right)^{2} \left(\Im{a}\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{atan_{2}}{\left (1458 \Re{a} \Im{a},729 \left(\Re{a}\right)^{2} - 729 \left(\Im{a}\right)^{2} + 108 \right )} \right )} - \frac{27 \Re{a}}{2}\right)^{2}}}$$