Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\left(-\sqrt{y^{4}+20}+y^{2}\right)^{2}}{4}\text{, }&arg(\frac{-\sqrt{y^{4}+20}+y^{2}}{2})<\pi \\x=\frac{\left(\sqrt{y^{4}+20}+y^{2}\right)^{2}}{4}\text{, }&arg(\frac{\sqrt{y^{4}+20}+y^{2}}{2})<\pi \end{matrix}\right.
Solve for y (complex solution)
y=-\sqrt{x^{-\frac{1}{2}}\left(x-5\right)}
y=\sqrt{x^{-\frac{1}{2}}\left(x-5\right)}\text{, }x\neq 0
Solve for x
\left\{\begin{matrix}\\x=\frac{\left(\sqrt{y^{4}+20}+y^{2}\right)^{2}}{4}\text{, }&\text{unconditionally}\\x=\frac{\left(-\sqrt{y^{4}+20}+y^{2}\right)^{2}}{4}\text{, }&\frac{-\sqrt{y^{4}+20}+y^{2}}{2}\geq 0\end{matrix}\right.
Solve for y
y=\frac{\sqrt{x-5}}{\sqrt[4]{x}}
y=-\frac{\sqrt{x-5}}{\sqrt[4]{x}}\text{, }x\geq 5
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