Ta có :
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(0=\left(x-5\right)^6-\left(x-5\right)^4\)
\(0=\left[\left(x-5\right)^2-1\right]\left(x-5\right)^4\)
Ta có các trường hợp :
TH1 : \(\left(x-5\right)^2-1=0\)
\(\Rightarrow\left(x-5\right)^2=1\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x-5\right)^2=1^2\\\left(x-5\right)^2=\left(-1\right)^2\end{matrix}\right.\)
TH2 : \(x-5=1\)
\(\Rightarrow x=6\left(TM\right)\)
TH3 : \(x-5=-1\)
\(\Rightarrow x=4\left(TM\right)\)
TH4 : \(\left(x-5\right)^4=0\)
\(\Rightarrow x-5=0\)
\(\Rightarrow x=5\left(TM\right)\)
Vậy \(x\in\left\{4,5,6\right\}\) là giá trị cần tìm
