Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{\sqrt{9+18y^{2}-3y^{4}}}{6y}+\frac{y}{2}+\frac{1}{2y}\text{; }x=\frac{\sqrt{9+18y^{2}-3y^{4}}}{6y}+\frac{y}{2}+\frac{1}{2y}\text{, }&y\neq 0\\x=0\text{, }&y=0\end{matrix}\right.
Solve for y (complex solution)
y=-\sqrt[3]{x}\sqrt[3]{x^{2}-3}+x
y=e^{\frac{\pi i}{3}}\sqrt[3]{x}\sqrt[3]{x^{2}-3}+x
y=e^{\frac{5\pi i}{3}}\sqrt[3]{x}\sqrt[3]{x^{2}-3}+x
Solve for x
\left\{\begin{matrix}x=-\frac{\sqrt{3\left(3+6y^{2}-y^{4}\right)}-3y^{2}-3}{6y}\text{; }x=\frac{\sqrt{3}\left(\sqrt{3+6y^{2}-y^{4}}+\sqrt{3}y^{2}+\sqrt{3}\right)}{6y}\text{, }&y\neq 0\text{ and }|y|\leq \frac{\sqrt{2}+\sqrt{6}}{2}\sqrt[4]{3}\\x=0\text{, }&y=0\end{matrix}\right.
Solve for y
y=-\sqrt[3]{x^{3}-3x}+x
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