\(\left(x-2\right)^5=\left(x-2\right)^{10}\)
\(\Leftrightarrow\left(x-2\right)^5-\left(x-2\right)^{10}=0\)
\(\Leftrightarrow\left(x-2\right)^5\left[1-\left(x-2\right)^5\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^5=0\\1-\left(x-2\right)^5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^5=0\\\left(x-2\right)^5=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-2=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
(x-2)5=(x-2)10
(x-2)5=(x-2)5+5
(x-2)5=(x-2)5.(x-2)5
x-2 =x-2. (x-2)5
x-2.(x-2)5= x-2
(x-2)5 =x-2: x-2
(x-2)5 =1
Ta có a1=1 =>x-2=1 x=1+2
x=3
