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