\(\left(n-2\right)^6=\left(n-2\right)^8\)
\(\Leftrightarrow\left(n-2\right)^6-\left(n-2\right)^8=0\)
\(\Leftrightarrow\left(n-2\right)^6\left[1-\left(n-2\right)^2\right]=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\left(n-2\right)^6=0\\1-\left(n-2\right)^2=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}n-2=0\\n-2=1\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}n=2\\n=1\end{array}\right.\)