\(x^{100}=x^{50}\Leftrightarrow x^{100}-x^{50}=0\Leftrightarrow x^{50}\left(x^{50}-1\right)=0\Leftrightarrow\left\{{}\begin{matrix}x^{50}=0\\x^{50}=1\\x^{50}=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
