Question

Tìm x biết : ( x - 7 ) ^{x + 1} - ( x - 7 ) ^{x + 11} = 0

Answer 1

Ta có : 

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

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

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

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

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=8\\x=6\end{cases}}}\)

Vậy \(x=6\) hoặc \(x=8\)

Chúc bạn học tốt ~ 

Answer 2

x=6/x=8