\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\Rightarrow\left(x-7\right)^{x+1}=\left(x-7\right)^{x+11}\)
\(\Rightarrow x+1=x+11\)
\(\Rightarrow x+x=1+11\)
\(\Rightarrow2x=12\)
\(\Rightarrow x=12:2=6\)
Vậy x=6
Nhớ tick cho mình nha!
Ta có: \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
=> \(\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\)
=> \(\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{x+11}=0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x-7=0\\\left(x-7\right)^{x+11}=1\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=7\\x-7=1\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)
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