Đáp án:
$\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$
Giải thích các bước giải:
$(x-7)^{x+1}-(x-7)^{x+11}=0$
$⇔(x-7)^{x+1}-(x-7)^{x+1}.(x-7)^{10}=0$
$⇔(x-7)^{x+1}.[1-(x-7)^{10}]=0$
$⇔\left[ \begin{array}{l}(x-7)^{x+1}=0\\1-(x-7)^{10}=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x-7=0\\x-7=1\\x-7=-1\end{array} \right.$
$⇔\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$
