\(x^{2005}=x\Leftrightarrow x^{2005}-x=0\Leftrightarrow x\left(x^{2004}-1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x^{2004}-1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\\left\{{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\end{matrix}\right.\) vậy \(x=0;x=1;x=-1\)
\(x^{2005}=x^1\)
Vì \(2005\ne1\) nên \(x\in\left\{-1;0;1\right\}\).
Vậy..................
Chúc bạn học tốt!!!
\(x^{2005}=x\)
\(\Rightarrow x^{2005}-x=0\)
\(\Rightarrow x\left(x^{2004}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{2004}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{2004}=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\end{matrix}\right.\)
