Question

Tìm x bt:

(x-7)^x+1 - (x+7)^x+11 = 0

Giúp mk vs!!!!!!!!!

Thanks!!!!!!!!

Answer 1

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

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

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

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

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

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

Vậy....