\(\left(x-7\right)^{x+11}-\left(x-7\right)^{x+1}=0\)
\(\left(x-7\right)^{x+1}.\left(x-7\right)^{10}-\left(x-7\right)^{x+1}=0\)
\(\left(x-7\right)^{x+1}\left[\left(x-7\right)^{10}-1\right]=0\)
Th1 \(x-7=0\Rightarrow x=7\)
Th2 \(\left(x-7\right)^{10}-1=0\)
\(\left(x-7\right)^{10}=1\Rightarrow x-7=0\Leftrightarrow x=7\)
Vậy x=7