Question

Tìm x

\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

Answer 1

\(\Leftrightarrow\left(x-7\right)\left(x-6\right)\left(x-8\right)=0\)

hay \(x\in\left\{6;7;8\right\}\)

Answer 2

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=7\\\left[{}\begin{matrix}x-7=1\Rightarrow x=8\\x-7=-1\Rightarrow x=6\end{matrix}\right.\end{matrix}\right.\)

Vậy \(x=\left\{6;7;8\right\}\)