(x - 7)^x + 1 - (x - 7)^x + 11 = 0
(x - 7)^x . (x - 7) - (x - 7)^x . (x - 7)^11 = 0
(x - 7)^x . [(x - 7) - (x - 7)^11] = 0
=> (x - 7)^x = 0 hoặc [(x - 7) - (x - 7)^11] = 0
* TH1: (x - 7)^x = 0
=> x - 7 = 0
=> x = 0 + 7
=> x = 7
* TH2: [(x - 7) - (x - 7)^11] = 0
=> x - 7 = (x -7)^11
=> x - 7 = 1 hoặc x - 7 = 0
x - 7 = 1
=> x = 1 + 7
x = 8
x - 7 = 0 (TH1)
Vậy x = 7 hoặc x = 8.
\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-7\right)^x-\left(x-7\right)\left(x-7\right)^x\left(x-7\right)^{10}=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-7\right)^x\left[1-\left(x-7\right)^{10}\right]=0\)
\(\Leftrightarrow\left[\begin{matrix}x-7=0\left(1\right)\\\left(x-7\right)^x=0\left(2\right)\\1-\left(x-7\right)^{10}=0\left(3\right)\end{matrix}\right.\)
(1) và (2)=> x=7
(3)\(\Leftrightarrow\left(x-7\right)^{10}=1\Rightarrow x-7=\pm\sqrt[10]{1}=\pm1\Rightarrow\left[\begin{matrix}x=8\\x=6\end{matrix}\right.\)
Kết luận nghiệm: x={6,7,8}
