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- La ecuación:
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Ecuación 3^x=7
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Ecuación 2+3x=-7x-5
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Ecuación 3-x/3=x/2
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Ecuación 3/(x-5)+8/x=2
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- -20*x-6*y=4
- 2*x-15*y=-1
- 8*x+3*y=4
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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
$$4 \cdot 8 x 3 \frac{2 \cdot 2 \cdot 4 x 11 \cdot 2 x}{2 x_{2}} = -16$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$4 \cdot 8 x 3 \frac{2 \cdot 2 \cdot 4 x 11 \cdot 2 x}{2 x_{2}} = -16$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
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
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = \frac{x_{2}}{1056}$$
$$4 \cdot 8 x 3 \frac{2 \cdot 2 \cdot 4 x 11 \cdot 2 x}{2 x_{2}} = -16$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
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) /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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