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La ecuación:
Ecuación 6x+1=-4x
Ecuación x^2=-3
Ecuación 9-7(x+3)=5-6x
Ecuación 6/(x+8)=-3/4
Expresar {x} en función de y en la ecuación:
-11*x+9*y=-20
5*x-14*y=-15
-10*x+15*y=10
-9*x-6*y=12
Expresiones idénticas
(dos x) once ⋅(cuatro x) dos ⋅2:(2x2) tres ⋅(8x)4=− dieciséis .
(2x)11⋅(4x)2⋅2:(2x2)3⋅(8x)4 es igual a −16.
(dos x) once ⋅(cuatro x) dos ⋅2:(2x2) tres ⋅(8x)4 es igual a − dieciséis .
2x11⋅4x2⋅2:2x23⋅8x4=−16.

(2x)11⋅(4x)2⋅2:(2x2)3⋅(8x)4=−16. la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

2*x*11*4*x*2*2              
--------------*3*8*x*4 = -16
     2*x2

4 \cdot 8 x 3 \frac{2 \cdot 2 \cdot 4 x 11 \cdot 2 x}{2 x_{2}} = -16

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

4 \cdot 8 x 3 \frac{2 \cdot 2 \cdot 4 x 11 \cdot 2 x}{2 x_{2}} = -16

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

\frac{x_{2} \left(\frac{16896 x^{3}}{x_{2}} + 16\right)}{16896} = 0

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = 0

q = \frac{c}{a}

q = 0

v = \frac{d}{a}

v = \frac{x_{2}}{1056}

Fórmulas de Cardano-Vieta

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} = \frac{x_{2}}{1056}

Gráfica

Respuesta rápida [src]

                 ___________________                                              ___________________                             
     3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\     3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\
     \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   I*\/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|
                                        \           3           /                                        \           3           /
x1 = ------------------------------------------------------------ + --------------------------------------------------------------
                                 132                                                             132

x_{1} = \frac{\sqrt[3]{2178} i \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132} + \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132}

       /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                             
       |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\
       |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------|
       |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /
x2 = I*|- ------------------------------------------------------------ - -----------------------------------------------------------------| - ------------------------------------------------------------ + -----------------------------------------------------------------
       \                              264                                                                88                               /                               264                                                                88

x_{2} = i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}

       /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                             
       |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\
       |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------|
       |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /
x3 = I*|- ------------------------------------------------------------ + -----------------------------------------------------------------| - ------------------------------------------------------------ - -----------------------------------------------------------------
       \                              264                                                                88                               /                               264                                                                88

x_{3} = i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}

x3 = i*(-2178^(1/3)*(re(x2)^2 + im(x2)^2)^(1/6)*sin(atan2(-im(x2, -re(x2))/3)/264 + 242^(1/3)*3^(1/6)*(re(x2)^2 + im(x2)^2)^(1/6)*cos(atan2(-im(x2), -re(x2))/3)/88) - 242^(1/3)*3^(1/6)*(re(x2)^2 + im(x2)^2)^(1/6)*sin(atan2(-im(x2), -re(x2))/3)/88 - 2178^(1/3)*(re(x2)^2 + im(x2)^2)^(1/6)*cos(atan2(-im(x2), -re(x2))/3)/264)

Suma y producto de raíces [src]

suma

            ___________________                                              ___________________                                  /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                                  /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                             
3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\     3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\     |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\     |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\
\/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   I*\/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|     |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------|     |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------|
                                   \           3           /                                        \           3           /     |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /     |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /
------------------------------------------------------------ + -------------------------------------------------------------- + I*|- ------------------------------------------------------------ - -----------------------------------------------------------------| - ------------------------------------------------------------ + ----------------------------------------------------------------- + I*|- ------------------------------------------------------------ + -----------------------------------------------------------------| - ------------------------------------------------------------ - -----------------------------------------------------------------
                            132                                                             132                                   \                              264                                                                88                               /                               264                                                                88                                    \                              264                                                                88                               /                               264                                                                88

\left(\left(\frac{\sqrt[3]{2178} i \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132} + \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132}\right) + \left(i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}\right)\right) + \left(i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}\right)

  /              ___________________                                                 ___________________                             \     /              ___________________                                                 ___________________                             \                 ___________________                             
  |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|     |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|     3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\
  |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||     |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   I*\/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|
  |                                     \           3           /                                           \           3           /|     |                                     \           3           /                                           \           3           /|                                        \           3           /
I*|- ------------------------------------------------------------ - -----------------------------------------------------------------| + I*|- ------------------------------------------------------------ + -----------------------------------------------------------------| + --------------------------------------------------------------
  \                              264                                                                88                               /     \                              264                                                                88                               /                                132

i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) + i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) + \frac{\sqrt[3]{2178} i \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132}

producto

/            ___________________                                              ___________________                             \ /  /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                             \ /  /              ___________________                                                 ___________________                             \               ___________________                                                 ___________________                             \
|3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\     3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\| |  |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\| |  |  3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|   3 ______ 6 /   2         2         /atan2(-im(x2), -re(x2))\   6 ___ 3 _____ 6 /   2         2         /atan2(-im(x2), -re(x2))\|
|\/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   I*\/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|| |  |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------|| |  |  \/ 2178 *\/  im (x2) + re (x2) *sin|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *cos|-----------------------||   \/ 2178 *\/  im (x2) + re (x2) *cos|-----------------------|   \/ 3 *\/ 242 *\/  im (x2) + re (x2) *sin|-----------------------||
|                                   \           3           /                                        \           3           /| |  |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /| |  |                                     \           3           /                                           \           3           /|                                      \           3           /                                           \           3           /|
|------------------------------------------------------------ + --------------------------------------------------------------|*|I*|- ------------------------------------------------------------ - -----------------------------------------------------------------| - ------------------------------------------------------------ + -----------------------------------------------------------------|*|I*|- ------------------------------------------------------------ + -----------------------------------------------------------------| - ------------------------------------------------------------ - -----------------------------------------------------------------|
\                            132                                                             132                              / \  \                              264                                                                88                               /                               264                                                                88                               / \  \                              264                                                                88                               /                               264                                                                88                               /

\left(\frac{\sqrt[3]{2178} i \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132} + \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{132}\right) \left(i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}\right) \left(i \left(- \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264} + \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88}\right) - \frac{\sqrt[3]{242} \sqrt[6]{3} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{88} - \frac{\sqrt[3]{2178} \sqrt[6]{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{264}\right)

                       /                                                                                                                                  /          im(x2)              /atan2(-im(x2), -re(x2))\\\
                       |                                                                                                                              3*I*|- ---------------------- + sin|-----------------------|||
                       |                                     /atan2(-im(x2), -re(x2))\                                                                    |     ___________________      \           3           /||
   ___________________ |                                3*cos|-----------------------|                                                                    |    /   2         2                                    ||
  /   2         2      |   3/atan2(-im(x2), -re(x2))\        \           3           /        3/atan2(-im(x2), -re(x2))\           3*re(x2)               \  \/  im (x2) + re (x2)                                /|
\/  im (x2) + re (x2) *|cos |-----------------------| - ------------------------------ - I*sin |-----------------------| - ------------------------ + -------------------------------------------------------------|
                       |    \           3           /                 4                        \           3           /        ___________________                                 4                              |
                       |                                                                                                       /   2         2                                                                     |
                       \                                                                                                   4*\/  im (x2) + re (x2)                                                                 /
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                                                                                                        1056

\frac{\sqrt{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \left(\frac{3 i \left(\sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)} - \frac{\operatorname{im}{\left(x_{2}\right)}}{\sqrt{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}}\right)}{4} - i \sin^{3}{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)} + \cos^{3}{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)} - \frac{3 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},- \operatorname{re}{\left(x_{2}\right)} \right)}}{3} \right)}}{4} - \frac{3 \operatorname{re}{\left(x_{2}\right)}}{4 \sqrt{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}}\right)}{1056}

sqrt(im(x2)^2 + re(x2)^2)*(cos(atan2(-im(x2), -re(x2))/3)^3 - 3*cos(atan2(-im(x2), -re(x2))/3)/4 - i*sin(atan2(-im(x2), -re(x2))/3)^3 - 3*re(x2)/(4*sqrt(im(x2)^2 + re(x2)^2)) + 3*i*(-im(x2)/sqrt(im(x2)^2 + re(x2)^2) + sin(atan2(-im(x2), -re(x2))/3))/4)/1056

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Expresiones idénticas

(2x)11⋅(4x)2⋅2:(2x2)3⋅(8x)4=−16. la ecuación

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