\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\Rightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-7\right)^{x-1}=0\\1-\left(x-7\right)^{10}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=0\\\left(x-7\right)^{10}=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=7\\\left(x-7\right)^{10}=\left(\pm1\right)^{10}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=7\\x-7=1\\x-7=-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=7\\x=8\\x=6\end{cases}}\)
P/S: 2 dòng cuối bn thay \(\hept{\begin{cases}\\\\\end{cases}}\)thành \(\orbr{\begin{cases}\\\end{cases}}\)nha