\(\left(3x-1\right)^2=\left(x-1\right)^2\)
=\(\left(3x-1\right)^2-\left(x-1\right)^2=0\)
=\(\left(3x-1+x-1\right)\left(3x-1-x+1\right)=0\)
=\(\left(4x-2\right)2x=0\)
=>\(\left[{}\begin{matrix}4x-2=0\\2x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=0\end{matrix}\right.\)
\(\left(3x-1\right)^2=\left(x-1\right)^2\)
\(\Leftrightarrow\left(3x-1\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(3x-1-x+1\right)\left(3x-1+x-1\right)=0\)
\(\Leftrightarrow2x\left(4x-2\right)=0\)
\(\Leftrightarrow4x\left(2x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\end{matrix}\right.\)
