\(c^4-2\left(a^2+b^2\right)c^2+\left(a^2+b^2\right)^2=a^2b^2\)
\(\Leftrightarrow\left(a^2+b^2-c^2\right)^2=a^2b^2\)
\(\Leftrightarrow\left[{}\begin{matrix}a^2+b^2-c^2=ab\\a^2+b^2+c^2=-ab\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}cosC=\frac{a^2+b^2-c^2}{2ab}=\frac{ab}{2ab}=\frac{1}{2}\\cosC=\frac{a^2+b^2-c^2}{2ab}=\frac{-ab}{2ab}=-\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}C=60^0\\C=120^0\end{matrix}\right.\)
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