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- La ecuación:
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Ecuación x^2-13*x+22=0
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Ecuación (-1+y)+2*y+4=0
- Ecuación 2*x+y=7
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
- (dos x+y- tres)^ dos +(y-x^2)^ cuatro = cero
- (2x más y menos 3) al cuadrado más (y menos x al cuadrado ) en el grado 4 es igual a 0
- (dos x más y menos tres) en el grado dos más (y menos x al cuadrado ) en el grado cuatro es igual a cero
- (2x+y-3)2+(y-x2)4=0
- 2x+y-32+y-x24=0
- (2x+y-3)²+(y-x²)⁴=0
- (2x+y-3) en el grado 2+(y-x en el grado 2) en el grado 4=0
- 2x+y-3^2+y-x^2^4=0
- (2x+y-3)^2+(y-x^2)^4=O
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Expresiones semejantes
- (2x+y+3)^2+(y-x^2)^4=0
- (2x+y-3)^2-(y-x^2)^4=0
- (2x+y-3)^2+(y+x^2)^4=0
- (2x-y-3)^2+(y-x^2)^4=0
(2x+y-3)^2+(y-x^2)^4=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
4
2 / 2\
(2*x + y - 3) + \y - x / = 0
$$\left(- x^{2} + y\right)^{4} + \left(\left(2 x + y\right) - 3\right)^{2} = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
/ _______________________________________________________________________ \ _______________________________________________________________________ / _______________________________________________________________________ \ _______________________________________________________________________ / ______________________________________________________________________ \ ______________________________________________________________________ / ______________________________________________________________________ \ ______________________________________________________________________
| / 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 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| 2 2 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| 2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| 2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/|
re (x) - im (x) + I*|- - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------| + re (x) - im (x) + I*|- + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------| + re (x) - im (x) + I*|- - - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------| + re (x) - im (x) + I*|- - + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------|
\2 \ 2 / / \ 2 / \2 \ 2 / / \ 2 / \ 2 \ 2 / / \ 2 / \ 2 \ 2 / / \ 2 /
$$\left(\left(\left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) + \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)\right) + \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)\right) + \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)$$
=
/ _______________________________________________________________________ \ / _______________________________________________________________________ \ / ______________________________________________________________________ \ / ______________________________________________________________________ \
| / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
2 2 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| |
- 4*im (x) + 4*re (x) + I*|- + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| + I*|- - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| + I*|- - + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| + I*|- - - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)|
\2 \ 2 / / \2 \ 2 / / \ 2 \ 2 / / \ 2 \ 2 / /
$$i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
producto
/ / _______________________________________________________________________ \ _______________________________________________________________________ \ / / _______________________________________________________________________ \ _______________________________________________________________________ \ / / ______________________________________________________________________ \ ______________________________________________________________________ \ / / ______________________________________________________________________ \ ______________________________________________________________________ \ | | / 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 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/|| | 2 2 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/|| | 2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/|| | 2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/|| |re (x) - im (x) + I*|- - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------||*|re (x) - im (x) + I*|- + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------||*|re (x) - im (x) + I*|- - - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------||*|re (x) - im (x) + I*|- - + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------|| \ \2 \ 2 / / \ 2 // \ \2 \ 2 / / \ 2 // \ \ 2 \ 2 / / \ 2 // \ \ 2 \ 2 / / \ 2 //
$$\left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)$$
=
8 8 2 2 2 6 6 2 4 4 3 5 7 7 5 3 9 + im (x) + re (x) - 12*re(x) - 4*im (x) + 4*re (x) - 28*im (x)*re (x) - 28*im (x)*re (x) - 12*I*im(x) + 70*im (x)*re (x) - 56*I*im (x)*re (x) - 8*I*im (x)*re(x) + 8*I*re (x)*im(x) + 8*I*im(x)*re(x) + 56*I*im (x)*re (x)
$$\left(\operatorname{re}{\left(x\right)}\right)^{8} + 8 i \left(\operatorname{re}{\left(x\right)}\right)^{7} \operatorname{im}{\left(x\right)} - 28 \left(\operatorname{re}{\left(x\right)}\right)^{6} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 56 i \left(\operatorname{re}{\left(x\right)}\right)^{5} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 70 \left(\operatorname{re}{\left(x\right)}\right)^{4} \left(\operatorname{im}{\left(x\right)}\right)^{4} + 56 i \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{5} - 28 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{6} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 8 i \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{7} + 8 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 12 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{8} - 4 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 12 i \operatorname{im}{\left(x\right)} + 9$$
9 + im(x)^8 + re(x)^8 - 12*re(x) - 4*im(x)^2 + 4*re(x)^2 - 28*im(x)^2*re(x)^6 - 28*im(x)^6*re(x)^2 - 12*i*im(x) + 70*im(x)^4*re(x)^4 - 56*i*im(x)^3*re(x)^5 - 8*i*im(x)^7*re(x) + 8*i*re(x)^7*im(x) + 8*i*im(x)*re(x) + 56*i*im(x)^5*re(x)^3
Respuesta rápida
[src]
/ _______________________________________________________________________ \ _______________________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
2 2 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/|
y1 = re (x) - im (x) + I*|- - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------|
\2 \ 2 / / \ 2 /
$$y_{1} = - \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
/ _______________________________________________________________________ \ _______________________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
2 2 |1 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\-3 + re (x) - im (x) + 2*re(x), -1/4 - 2*im(x) - 2*im(x)*re(x)/|
y2 = re (x) - im (x) + I*|- + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *sin|---------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 - 2*im(x) - 2*im(x)*re(x)) + \-3 + re (x) - im (x) + 2*re(x)/ *cos|---------------------------------------------------------------------|
\2 \ 2 / / \ 2 /
$$y_{2} = \sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \operatorname{re}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 3,- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
/ ______________________________________________________________________ \ ______________________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/|
y3 = re (x) - im (x) + I*|- - - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| - \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------|
\ 2 \ 2 / / \ 2 /
$$y_{3} = - \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
/ ______________________________________________________________________ \ ______________________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
2 2 | 1 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/| | 4 / 2 / 2 2 \ |atan2\3 + im (x) - re (x) - 2*re(x), -1/4 + 2*im(x) + 2*im(x)*re(x)/|
y4 = re (x) - im (x) + I*|- - + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *sin|--------------------------------------------------------------------| + 2*im(x)*re(x)| + \/ (-1/4 + 2*im(x) + 2*im(x)*re(x)) + \3 + im (x) - re (x) - 2*re(x)/ *cos|--------------------------------------------------------------------|
\ 2 \ 2 / / \ 2 /
$$y_{4} = \sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4}\right)^{2} + \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} - 2 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2} + 3,2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(x\right)} - \frac{1}{4} \right)}}{2} \right)} + 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \frac{1}{2}\right) + \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
y4 = ((2*re(x)*im(x) + 2*im(x) - 1/4)^2 + (-re(x)^2 - 2*re(x) + im(x)^2 + 3)^2)^(1/4)*cos(atan2(-re(x)^2 - 2*re(x) + im(x^2 + 3, 2*re(x)*im(x) + 2*im(x) - 1/4)/2) + i*(((2*re(x)*im(x) + 2*im(x) - 1/4)^2 + (-re(x)^2 - 2*re(x) + im(x)^2 + 3)^2)^(1/4)*sin(atan2(-re(x)^2 - 2*re(x) + im(x)^2 + 3, 2*re(x)*im(x) + 2*im(x) - 1/4)/2) + 2*re(x)*im(x) - 1/2) + re(x)^2 - im(x)^2)