\(\Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)

=> (x-7)^x+1  +  1.[1-(x-7)^10] = 0

=> x-7 = 0 hoặc 1-(x-7)^10 = 0

=> x=7 hoặc x = 8 hoặc x = 6 

k mk nha

=> (x-7)^x+1(1 - (x-7)¹⁰) = 0

=> (x-7)^x+1 = 0

=> x-7 = 0 => x = 7

hoặc 1 - (x-7)¹⁰ = 0

=> (x-7)¹⁰ = 1

=> x-7 = 1

=> x = 8

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

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

\(\Leftrightarrow\orbr{\begin{cases}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{10}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-7=0\\\left(x-7\right)^{10}=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=7\\x=8\end{cases}}\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x-7^{x+1}=0\\1-\left(x-y\right)^{10}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-7=0\\\left(x-y\right)^{10}=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=7\\x=8\end{cases}}\)

Cái này ms đúng 

\(\Leftrightarrow\left(x-7\right)\left(x-6\right)\left(x-8\right)=0\)

hay \(x\in\left\{6;7;8\right\}\)

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

\(\Leftrightarrow\left(x-7\right)^{x+1}.\left(1-\left(x-7\right)^{10}\right)=0\)

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

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

Vậy \(x=\left\{6;7;8\right\}\)

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

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

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

Th1  \(x-7=0\Rightarrow x=7\)

Th2  \(\left(x-7\right)^{10}-1=0\)

\(\left(x-7\right)^{10}=1\Rightarrow x-7=0\Leftrightarrow x=7\)

Vậy x=7

bài toán này cực khó

Bài này lớp 6 ak khó nhỉ 

Dễ quá là dễ

x=7

Nhớ cho mình nha

đề sai