Evaluate (complex solution)
\frac{x^{2}+y^{2}}{xy}=192904321000\text{ and }192904321000=\left(xy\right)^{5}
Solve for x
\left\{\begin{matrix}x=\frac{\left(\sqrt{192904320998}+96452160500\sqrt{192904321002}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&y=\frac{\left(\sqrt{192904321002}-\sqrt{192904320998}\right)\sqrt[10]{192904321000}}{2}\text{ and }\left(96452160500-\sqrt{9303019265117760249999}\right)\sqrt[5]{192904321000}\geq 0\\x=-\frac{\left(\sqrt{192904320998}+96452160500\sqrt{192904321002}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&y=-\frac{\left(\sqrt{192904321002}-\sqrt{192904320998}\right)\sqrt[10]{192904321000}}{2}\text{ and }\left(96452160500-\sqrt{9303019265117760249999}\right)\sqrt[5]{192904321000}\geq 0\\x=\frac{\left(96452160500\sqrt{192904321002}-\sqrt{192904320998}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&\left(96452160500\sqrt{192904321002}-\sqrt{192904320998}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}\neq 0\text{ and }y=\frac{\left(\sqrt{192904320998}+\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\\x=-\frac{\left(96452160500\sqrt{192904321002}-\sqrt{192904320998}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&\left(96452160500\sqrt{192904321002}-\sqrt{192904320998}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}\neq 0\text{ and }y=-\frac{\left(\sqrt{192904320998}+\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=-\frac{\left(\sqrt{192904320998}+25681\sqrt{2721084412018590901754682}-96452160500\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\text{, }&\left(\sqrt{192904320998}+25681\sqrt{2721084412018590901754682}-96452160500\sqrt{192904321002}\right)\sqrt[10]{192904321000}\neq 0\text{ and }x=\frac{\left(\sqrt{192904320998}+\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\\y=\frac{\left(\sqrt{192904320998}+25681\sqrt{2721084412018590901754682}-96452160500\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\text{, }&\left(\sqrt{192904320998}+25681\sqrt{2721084412018590901754682}-96452160500\sqrt{192904321002}\right)\sqrt[10]{192904321000}\neq 0\text{ and }x=-\frac{\left(\sqrt{192904320998}+\sqrt{192904321002}\right)\sqrt[10]{192904321000}}{2}\\y=-\frac{\left(\sqrt{192904320998}+96452160500\sqrt{192904321002}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&x=-\frac{\left(\sqrt{192904321002}-\sqrt{192904320998}\right)\sqrt[10]{192904321000}}{2}\text{ and }\left(96452160500-\sqrt{9303019265117760249999}\right)\sqrt[5]{192904321000}\geq 0\\y=\frac{\left(\sqrt{192904320998}+96452160500\sqrt{192904321002}-25681\sqrt{2721084412018590901754682}\right)\sqrt[10]{192904321000}}{2}\text{, }&x=\frac{\left(\sqrt{192904321002}-\sqrt{192904320998}\right)\sqrt[10]{192904321000}}{2}\text{ and }\left(96452160500-\sqrt{9303019265117760249999}\right)\sqrt[5]{192904321000}\geq 0\end{matrix}\right.
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