2(xy+y)*y^+x*(y⁴+1)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
$$y_{1} = 0$$
___ ___
\/ 2 I*\/ 2
y2 = - ----- + -------
2 2
$$y_{2} = - \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}$$
___ ___
\/ 2 I*\/ 2
y3 = ----- - -------
2 2
$$y_{3} = \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}$$
___ ___
\/ 2 I*\/ 2
y4 = - ----- - -------
2 2
$$y_{4} = - \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}$$
___ ___
\/ 2 I*\/ 2
y5 = ----- + -------
2 2
$$y_{5} = \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}$$
y5 = sqrt(2)/2 + sqrt(2)*i/2
Suma y producto de raíces
[src]
___ ___ ___ ___ ___ ___ ___ ___
\/ 2 I*\/ 2 \/ 2 I*\/ 2 \/ 2 I*\/ 2 \/ 2 I*\/ 2
- ----- + ------- + ----- - ------- + - ----- - ------- + ----- + -------
2 2 2 2 2 2 2 2
$$\left(\left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right) + \left(\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right) + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right)\right) + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)$$
$$0$$
/ ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\
| \/ 2 I*\/ 2 | |\/ 2 I*\/ 2 | | \/ 2 I*\/ 2 | |\/ 2 I*\/ 2 |
0*|- ----- + -------|*|----- - -------|*|- ----- - -------|*|----- + -------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$0 \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right) \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right) \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right) \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)$$
$$0$$