\(\left(x-2\right)^{1000}=\left(x-2\right)^{2000}\)
\(\Leftrightarrow\left(x-2\right)^{1000}-\left(x-2\right)^{2000}=0\)
\(\Leftrightarrow\left(x-2\right)^{1000}\cdot\left[1-\left(x-2\right)^{1000}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-2\right)^{1000}=0\\1-\left(x-2\right)^{1000}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^{1000}=1\Rightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\end{matrix}\right.\)
Vậy.........................
Ta có các số sau có số mũ bao nhiêu vẫn là chính số đó là :0;1
Nếu x-2=0 :
x-2=0
x=0+2
x=2
Nếu x-2=1 :
x-2=1
x=1+2
x=3
Vậy x\(\in\){2;3}
\(\left(x-2\right)^{1000}=\left(x-2\right)^{2000}\)
\(\Rightarrow\left(x-2\right)^{2000}-\left(x-2\right)^{1000}=0\)
\(\Rightarrow\left(x-2\right)^{1000}\left[\left(x-2\right)^{1000}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^{1000}=0\\\left(x-2\right)^{1000}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\end{matrix}\right.\)
