\(x^{2010}=x\)
\(\Rightarrow x^{2010}-x=0\)
\(\Rightarrow x.\left(x^{2009}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{2009}-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x^{2009}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{0;1\right\}.\)
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