\(\left(x+7\right)^{x+1}-\left(x+7\right)^{x+11}\)

\((x+7)^{x+1}+[1-\left(x+7\right)^{10}]=0\)

Nên \(\left(x+7\right)^{x+1}=0\) hoặc \(1-\left(x+7\right)^{10}=0\)

Mà \(1< \left(x+7\right)^{10}\)

Do đó \(\left(x+7\right)^{x+1}=0\)

Suy ra \(x+7=0\)

Vậy x=-7