x^2*y^t-y^2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
/ -1 \ / -1 \
| ------| | ------|
| -2 + t| | -2 + t|
|/ 2\ | |/ 2\ |
y1 = I*im\\x / / + re\\x / /
$$y_{1} = \operatorname{re}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)} + i \operatorname{im}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)}$$
y1 = re((x^2)^(-1/(t - 2))) + i*im((x^2)^(-1/(t - 2)))
Suma y producto de raíces
[src]
/ -1 \ / -1 \
| ------| | ------|
| -2 + t| | -2 + t|
|/ 2\ | |/ 2\ |
I*im\\x / / + re\\x / /
$$\operatorname{re}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)} + i \operatorname{im}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)}$$
/ -1 \ / -1 \
| ------| | ------|
| -2 + t| | -2 + t|
|/ 2\ | |/ 2\ |
I*im\\x / / + re\\x / /
$$\operatorname{re}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)} + i \operatorname{im}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)}$$
/ -1 \ / -1 \
| ------| | ------|
| -2 + t| | -2 + t|
|/ 2\ | |/ 2\ |
I*im\\x / / + re\\x / /
$$\operatorname{re}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)} + i \operatorname{im}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)}$$
/ -1 \ / -1 \
| ------| | ------|
| -2 + t| | -2 + t|
|/ 2\ | |/ 2\ |
I*im\\x / / + re\\x / /
$$\operatorname{re}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)} + i \operatorname{im}{\left(\left(x^{2}\right)^{- \frac{1}{t - 2}}\right)}$$
i*im((x^2)^(-1/(-2 + t))) + re((x^2)^(-1/(-2 + t)))