Question

Tìm x :

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

Answer 1

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

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

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

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

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

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

Vậy ....