$\text{( x - 7 )}$ $^{x+1}-$ $x+7^{x+11}=0$
$⇔(x-7)^{x+1}[1-($ $x-7)^{x+10}]=0$
$⇔(x-7)^{x+1}=0$ $\text{hoặc}$ ( $x-7)^{x+10}=1$
$\text{trường hợp 1 :}x+7^{x+1}=0 ⇔ x-7=0 ⇔ x=7$
$\text{trường hợp 2 :}x+7^{x+10}=1$
$\text{trường hợp 1 : nếu x = 2k}$ \(\left[ \begin{array}{l}x-7=1\\x-7=-1\end{array} \right.⇔\) \(\left[ \begin{array}{l}x=8(tm)\\x=6(tm)\end{array} \right.\)
$\text{Nếu x = 2k + 1 }$
$\text{⇒ x - 7 = 1}$
$\text{⇒ x = 8 ( loại )}$
$\text{Vậy x ∈ { 6 , 7 , 8 }}$
