Question

$$\left. \begin{array} { l } { y = 2 p x + p ^ { 4 } x ^ { 2 } } \end{array} \right.$$

Solve for x (complex solution)

$\left\{\begin{matrix}x=-\frac{\sqrt{p^{2}\left(yp^{2}+1\right)}+p}{p^{4}}\text{; }x=\frac{\sqrt{p^{2}\left(yp^{2}+1\right)}-p}{p^{4}}\text{, }&p\neq 0\\x\in \mathrm{C}\text{, }&p=0\text{ and }y=0\end{matrix}\right.$

Solve for x

$\left\{\begin{matrix}x=-\frac{\sqrt{yp^{2}+1}+1}{p^{3}}\text{; }x=\frac{\sqrt{yp^{2}+1}-1}{p^{3}}\text{, }&p\neq 0\text{ and }y\geq -\frac{1}{p^{2}}\\x\in \mathrm{R}\text{, }&p=0\text{ and }y=0\end{matrix}\right.$