Question

Tìm x biết \(\left(x-1\right)^{x+1}-\left(x-1\right)^{x+10}=0\) nãy mình thiếu x+10

Answer 1

\(\Leftrightarrow\left(x-1\right)^{x+1}\left[1-\left(x-1\right)^9\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^{x+1}=0\\\left(x-1\right)^9=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-1=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)