x^3-5*x-3=0 (уравнение)

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    Найду корень уравнения: x^3-5*x-3=0

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     3              
    x  - 5*x - 3 = 0
    $$x^{3} - 5 x - 3 = 0$$
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             /                 1                  \     /    /                 1                  \                                                       \                                                       
         5*re|------------------------------------|     |5*im|------------------------------------|            /    /  _____\\             /    /  _____\\|            /    /  _____\\             /    /  _____\\
             |                     _______________|     |    |                     _______________|            |    |\/ 771 ||             |    |\/ 771 |||            |    |\/ 771 ||             |    |\/ 771 ||
             |/          ___\     /         _____ |     |    |/          ___\     /         _____ |            |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||
             ||  1   I*\/ 3 |    /  3   I*\/ 771  |     |    ||  1   I*\/ 3 |    /  3   I*\/ 771  |     ___    |    \   27  /|     ____    |    \   27  /||     ___    |    \   27  /|     ____    |    \   27  /|
             ||- - - -------|*3 /   - + --------- |     |    ||- - - -------|*3 /   - + --------- |   \/ 5 *cos|-------------|   \/ 15 *sin|-------------||   \/ 5 *sin|-------------|   \/ 15 *cos|-------------|
             \\  2      2   / \/    2       18    /     |    \\  2      2   / \/    2       18    /            \      3      /             \      3      /|            \      3      /             \      3      /
    x1 = ------------------------------------------ + I*|------------------------------------------ - ------------------------ - -------------------------| + ------------------------ - -------------------------
                             3                          \                    3                                   2                           6            /              2                           6            
    $$x_{1} = - \frac{\sqrt{15}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} + \frac{5}{3} \Re{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}}\right)} + \frac{\sqrt{5}}{2} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} + i \left(- \frac{\sqrt{5}}{2} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} - \frac{\sqrt{15}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} + \frac{5}{3} \Im{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}}\right)}\right)$$
             /                 1                  \     /    /                 1                  \                                                       \                                                       
         5*re|------------------------------------|     |5*im|------------------------------------|            /    /  _____\\             /    /  _____\\|            /    /  _____\\             /    /  _____\\
             |                     _______________|     |    |                     _______________|            |    |\/ 771 ||             |    |\/ 771 |||            |    |\/ 771 ||             |    |\/ 771 ||
             |/          ___\     /         _____ |     |    |/          ___\     /         _____ |            |atan|-------||             |atan|-------|||            |atan|-------||             |atan|-------||
             ||  1   I*\/ 3 |    /  3   I*\/ 771  |     |    ||  1   I*\/ 3 |    /  3   I*\/ 771  |     ___    |    \   27  /|     ____    |    \   27  /||     ___    |    \   27  /|     ____    |    \   27  /|
             ||- - + -------|*3 /   - + --------- |     |    ||- - + -------|*3 /   - + --------- |   \/ 5 *cos|-------------|   \/ 15 *sin|-------------||   \/ 5 *sin|-------------|   \/ 15 *cos|-------------|
             \\  2      2   / \/    2       18    /     |    \\  2      2   / \/    2       18    /            \      3      /             \      3      /|            \      3      /             \      3      /
    x2 = ------------------------------------------ + I*|------------------------------------------ + ------------------------ - -------------------------| - ------------------------ - -------------------------
                             3                          \                    3                                   2                           6            /              2                           6            
    $$x_{2} = \frac{5}{3} \Re{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}}\right)} - \frac{\sqrt{15}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} - \frac{\sqrt{5}}{2} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} + i \left(\frac{5}{3} \Im{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}}\right)} - \frac{\sqrt{15}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )} + \frac{\sqrt{5}}{2} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{771}}{27} \right )} \right )}\right)$$
              _______________                         
             /         _____                          
            /  3   I*\/ 771               5           
    x3 = 3 /   - + ---------  + ----------------------
         \/    2       18              _______________
                                      /         _____ 
                                     /  3   I*\/ 771  
                                3*3 /   - + --------- 
                                  \/    2       18    
    $$x_{3} = \frac{5}{3 \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}} + \sqrt[3]{\frac{3}{2} + \frac{\sqrt{771} i}{18}}$$
    Численный ответ
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    x1 = -1.83424318431000
    x2 = -0.656620431047000
    x3 = 2.49086361536000