Question

(x-7) mũ x+1 - (x-7) mũ x+11 = 0                                                                                    Giúp mình với mọi người ơi 

Answer 1

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

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

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

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

=>\(\left[{}\begin{matrix}x-7=0\\x-7=-1\\x-7=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=6\\x=8\end{matrix}\right.\)