\(\left(x-1\right)^{2000}=\left(x-1\right)^{1998}\)
\(\Rightarrow\left(x-1\right)^{2000}-\left(x-1\right)^{1998}=0\)
\(\Rightarrow\left(x-1\right)^{1998}.\left(x-1\right)^2-\left(x-1\right)^{1998}=0\)
\(\Rightarrow\left(x-1\right)^{1998}.\left[\left(x-1\right)^2-1\right]=0\)
\(\Rightarrow\left(x-1\right)^{1998}\left[\left(x-1\right)^2-1^2\right]=0\)
\(\Rightarrow\left(x-1\right)^{1998}\left(x-1-1\right)\left(x-1+1\right)=0\)
\(\Rightarrow x\left(x-1\right)^{1998}.\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^{1998}=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=2\end{matrix}\right.\)
\(\left(x-1\right)^{2000}=\left(x-1\right)^{1998}\)
\(\Rightarrow\left(x-1\right)^{2000}-\left(x-1\right)^{1998}=0\)
\(\Rightarrow\left(x-1\right)^{1998}\left[\left(x-1\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^{2998}=0\\\left(x-1\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\end{matrix}\right.\)
