\(a.x^2=2x\Leftrightarrow x^2-2x=0\Leftrightarrow x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x_1=0\\x_2=2\end{matrix}\right.\)
\(b.x^{50}=x^2\Leftrightarrow x^{50}-x^2=0\Leftrightarrow x^2\left(x^{48}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x^{48}-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^{48}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x_1=0\\x_2=1\\x_3=-1\end{matrix}\right.\)
\(c.\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\Leftrightarrow\left(3x-1\right)^{10}-\left(3x-1\right)^{20}=0\)
\(\Leftrightarrow\left(3x-1\right)^{10}\left[1-\left(3x-1\right)^{10}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(3x-1\right)^{10}=0\\1-\left(3x-1\right)^{10}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\3x-1=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x_1=\dfrac{1}{3}\\x_2=\dfrac{2}{3}\end{matrix}\right.\)
