`(x-4)^4=(x-5)^6`
`=>(x-4)^6-(x-4)^4=0`
`=>(x-4)^4[(x-4)^2-1]=0`
`=>` $\left[ \begin{array}{l}x-4=0\\(x-4)^2=1\end{array} \right.$
`=>` $\left[ \begin{array}{l}x=4\\x-4=-1\\x-4=1\end{array} \right.$
`=>` $\left[ \begin{array}{l}x=4\\x=3\\x=5\end{array} \right.$
Vậy x=3 hoặc x=4 hoặc x=5
Ta có: \(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Leftrightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Leftrightarrow\left(x-5\right)^4\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-5\right)\cdot\left(x-5-1\right)\left(x-5+1\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-6\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-6=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)
Vậy: \(x\in\left\{4;5;6\right\}\)
