Câu hỏi của Trần Hoài khánh Trang

Question

Tìm x bt:

(x-7)x+1 - (x+7)x+11 = 0

Giúp mk vs!!!!!!!!!

Thanks!!!!!!!!

Trần Thị Hiền · Accepted Answer

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

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

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

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

$\Rightarrow\left[\begin{matrix}x-7=0\\left[\begin{matrix}x-7=1\x-7=-1\end{matrix}\right.\end{matrix}\right.$

$\Rightarrow\left[\begin{matrix}x=7\\left[\begin{matrix}x=8\x=6\end{matrix}\right.\end{matrix}\right.$

Vậy....Câu trả lời: $\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0$

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

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

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

$\Rightarrow\left[\begin{matrix}x-7=0\\left[\begin{matrix}x-7=1\x-7=-1\end{matrix}\right.\end{matrix}\right.$

$\Rightarrow\left[\begin{matrix}x=7\\left[\begin{matrix}x=8\x=6\end{matrix}\right.\end{matrix}\right.$

Vậy....