y-x^3=1 (уравнение)

Найду корень уравнения: y-x^3=1

Вы ввели

     3    
y - x  = 1

$$- x^{3} + y = 1$$

Быстрый ответ

        ________________________                                      ________________________                              
     6 /             2     2        /atan2(im(y), -1 + re(y))\     6 /             2     2        /atan2(im(y), -1 + re(y))\
x1 = \/  (-1 + re(y))  + im (y) *cos|------------------------| + I*\/  (-1 + re(y))  + im (y) *sin|------------------------|
                                    \           3            /                                    \           3            /

$$x_{1} = i \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}$$

       /     ________________________                                          ________________________                              \      ________________________                                          ________________________                              
       |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\
       |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------|
       |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /
x2 = I*|- --------------------------------------------------------- - ---------------------------------------------------------------| - --------------------------------------------------------- + ---------------------------------------------------------------
       \                              2                                                              2                               /                               2                                                              2                               

$$x_{2} = i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}$$

       /     ________________________                                          ________________________                              \      ________________________                                          ________________________                              
       |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\
       |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------|
       |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /
x3 = I*|- --------------------------------------------------------- + ---------------------------------------------------------------| - --------------------------------------------------------- - ---------------------------------------------------------------
       \                              2                                                              2                               /                               2                                                              2                               

$$x_{3} = i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}$$

Сумма и произведение корней

сумма

                                                                                                                            /     ________________________                                          ________________________                              \      ________________________                                          ________________________                                   /     ________________________                                          ________________________                              \      ________________________                                          ________________________                              
                                                                                                                            |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\     |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\
   ________________________                                      ________________________                                   |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------|     |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------|
6 /             2     2        /atan2(im(y), -1 + re(y))\     6 /             2     2        /atan2(im(y), -1 + re(y))\     |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /     |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /
\/  (-1 + re(y))  + im (y) *cos|------------------------| + I*\/  (-1 + re(y))  + im (y) *sin|------------------------| + I*|- --------------------------------------------------------- - ---------------------------------------------------------------| - --------------------------------------------------------- + --------------------------------------------------------------- + I*|- --------------------------------------------------------- + ---------------------------------------------------------------| - --------------------------------------------------------- - ---------------------------------------------------------------
                               \           3            /                                    \           3            /     \                              2                                                              2                               /                               2                                                              2                                    \                              2                                                              2                               /                               2                                                              2                               

$$\left(\left(i \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}\right) + \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right)\right) + \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right)$$

=

  /     ________________________                                          ________________________                              \     /     ________________________                                          ________________________                              \                                                              
  |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|     |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|                                                              
  |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||     |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||        ________________________                              
  |                                 \           3            /                                        \           3            /|     |                                 \           3            /                                        \           3            /|     6 /             2     2        /atan2(im(y), -1 + re(y))\
I*|- --------------------------------------------------------- + ---------------------------------------------------------------| + I*|- --------------------------------------------------------- - ---------------------------------------------------------------| + I*\/  (-1 + re(y))  + im (y) *sin|------------------------|
  \                              2                                                              2                               /     \                              2                                                              2                               /                                    \           3            /

$$i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) + i \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}$$

произведение

                                                                                                                          /  /     ________________________                                          ________________________                              \      ________________________                                          ________________________                              \ /  /     ________________________                                          ________________________                              \      ________________________                                          ________________________                              \
                                                                                                                          |  |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\| |  |  6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|   6 /             2     2        /atan2(im(y), -1 + re(y))\     ___ 6 /             2     2        /atan2(im(y), -1 + re(y))\|
/   ________________________                                      ________________________                              \ |  |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------|| |  |  \/  (-1 + re(y))  + im (y) *sin|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *cos|------------------------||   \/  (-1 + re(y))  + im (y) *cos|------------------------|   \/ 3 *\/  (-1 + re(y))  + im (y) *sin|------------------------||
|6 /             2     2        /atan2(im(y), -1 + re(y))\     6 /             2     2        /atan2(im(y), -1 + re(y))\| |  |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /| |  |                                 \           3            /                                        \           3            /|                                  \           3            /                                        \           3            /|
|\/  (-1 + re(y))  + im (y) *cos|------------------------| + I*\/  (-1 + re(y))  + im (y) *sin|------------------------||*|I*|- --------------------------------------------------------- - ---------------------------------------------------------------| - --------------------------------------------------------- + ---------------------------------------------------------------|*|I*|- --------------------------------------------------------- + ---------------------------------------------------------------| - --------------------------------------------------------- - ---------------------------------------------------------------|
\                               \           3            /                                    \           3            // \  \                              2                                                              2                               /                               2                                                              2                               / \  \                              2                                                              2                               /                               2                                                              2                               /

$$\left(i \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}\right) \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{2}\right)$$

=

                                   /                                                                                                                                          /           im(y)                 /atan2(im(y), -1 + re(y))\\                                \
                                   |                                                                                                                                      3*I*|--------------------------- + sin|------------------------||                                |
                                   |                                                                      /atan2(im(y), -1 + re(y))\                                          |   ________________________      \           3            /|                                |
   _______________________________ |                                                                 3*cos|------------------------|                                          |  /             2     2                                    |                                |
  /       2        2               |   3/atan2(im(y), -1 + re(y))\                 3                      \           3            /        3/atan2(im(y), -1 + re(y))\       \\/  (-1 + re(y))  + im (y)                                 /              3*re(y)           |
\/  1 + im (y) + re (y) - 2*re(y) *|cos |------------------------| - ----------------------------- - ------------------------------- - I*sin |------------------------| + ----------------------------------------------------------------- + -----------------------------|
                                   |    \           3            /        ________________________                  4                        \           3            /                                   4                                        ________________________|
                                   |                                     /             2     2                                                                                                                                                    /             2     2    |
                                   \                                 4*\/  (-1 + re(y))  + im (y)                                                                                                                                             4*\/  (-1 + re(y))  + im (y) /

$$\sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 2 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1} \left(\frac{3 i \left(\sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} + \frac{\operatorname{im}{\left(y\right)}}{\sqrt{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}}\right)}{4} - i \sin^{3}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} + \cos^{3}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)} - \frac{3 \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 1 \right)}}{3} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4 \sqrt{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} - \frac{3}{4 \sqrt{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}}\right)$$

Теорема Виета

перепишем уравнение
$$- x^{3} + y = 1$$
из
$$a x^{3} + b x^{2} + c x + d = 0$$
как приведённое кубическое уравнение
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - y + 1 = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
где
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = 1 - y$$
Формулы Виета
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = 1 - y$$