Evaluate (complex solution)
\frac{x^{2}+y^{2}}{xy}=192904321000000\text{ and }192904321000000=xy
Solve for x
\left\{\begin{matrix}x=41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\text{, }&y=6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\text{ and }74424154120942082000000000000-771617284000000\sqrt{9303019265117760249999999999}\geq 0\text{ and }41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\neq 0\text{ and }6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\neq 0\\x=20833500\sqrt{199399179398608792456174498369732853222222}+669812028592250000000\sqrt{192904321000002}-41548943500\sqrt{50133482121217702763225260984081218}-669812028592250000000\sqrt{192904320999998}\text{, }&y=6944500\sqrt{192904321000002}-6944500\sqrt{192904320999998}\text{ and }74424154120942082000000000000-771617284000000\sqrt{9303019265117760249999999999}\geq 0\text{ and }41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\neq 0\text{ and }6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\neq 0\\x=20833500\sqrt{199399179398608792456174498369732853222222}+41548943500\sqrt{50133482121217702763225260984081218}-669812028592250000000\sqrt{192904320999998}-669812028592250000000\sqrt{192904321000002}\text{, }&669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\neq 0\text{ and }y=-6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\\x=669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\text{, }&669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\neq 0\text{ and }y=6944500\sqrt{192904320999998}+6944500\sqrt{192904321000002}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=20833500\sqrt{199399179398608792456174498369732853222222}+41548943500\sqrt{50133482121217702763225260984081218}-669812028592250000000\sqrt{192904320999998}-669812028592250000000\sqrt{192904321000002}\text{, }&669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\neq 0\text{ and }x=-6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\\y=669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\text{, }&669812028592250000000\sqrt{192904320999998}+669812028592250000000\sqrt{192904321000002}-20833500\sqrt{199399179398608792456174498369732853222222}-41548943500\sqrt{50133482121217702763225260984081218}\neq 0\text{ and }x=6944500\sqrt{192904320999998}+6944500\sqrt{192904321000002}\\y=41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\text{, }&x=6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\text{ and }74424154120942082000000000000-771617284000000\sqrt{9303019265117760249999999999}\geq 0\text{ and }6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\neq 0\text{ and }41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\neq 0\\y=20833500\sqrt{199399179398608792456174498369732853222222}+669812028592250000000\sqrt{192904321000002}-41548943500\sqrt{50133482121217702763225260984081218}-669812028592250000000\sqrt{192904320999998}\text{, }&x=6944500\sqrt{192904321000002}-6944500\sqrt{192904320999998}\text{ and }74424154120942082000000000000-771617284000000\sqrt{9303019265117760249999999999}\geq 0\text{ and }6944500\sqrt{192904320999998}-6944500\sqrt{192904321000002}\neq 0\text{ and }41548943500\sqrt{50133482121217702763225260984081218}+669812028592250000000\sqrt{192904320999998}-20833500\sqrt{199399179398608792456174498369732853222222}-669812028592250000000\sqrt{192904321000002}\neq 0\end{matrix}\right.
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\frac{ y }{ x } + \frac{ x }{ y } = 250000 \times { 27778 }^{ 2 } =xy
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