Đáp án:
Giải thích các bước giải:
$\left(x-7\right)^{x-1}\:\:\:-\:\:\:\left(x-7\right)^{x+11}=0$
$(x-7)^{x+11}[ \dfrac{1}{\left(x-7\right)^{12}} -1]=0$
`<=>`\(\left[ \begin{array}{l}(x-7)^{x+11}=0\\\dfrac{1}{\left(x-7\right)^{12}} -1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x-7=0\\1-\left(x-7\right)^{12}=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=7\\-\left(x-7\right)^{12}=-1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=7\\\left(x-7\right)^{12}=1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=7\\x=8,\:x=6\end{array} \right.\)
Vậy `x=6;7;8`
