\(x^{100}=x^2\Leftrightarrow x^{100}-x^2=0\Leftrightarrow x^2\left(x^{98}-1\right)=0\Rightarrow\left[{}\begin{matrix}x^2=0\\x^{98}-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x^{98}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
\(x^{100}=x^2\)
\(\Rightarrow x^{100}-x^2=0\)
\(\Rightarrow x^2.\left(x^{98}-1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=0\\x^{98}-1=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x^{98}=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x=\pm1\end{matrix}\right.\)
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