x + x\(^2\) = x\(^2\) + x\(^3\)
x + x\(^2\) - x\(^2\) - x\(^3\) = 0
x - x\(^3\) = 0
=> x = 0
\(x+x^2=x^2+x^3\)
\(\Leftrightarrow x+x^2-\left(x^2+x^3\right)=0\)
\(\Leftrightarrow x-x^3=0\)
\(\Leftrightarrow x.\left(1-x^2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\1-x^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
Vậy : \(x\in\left\{0,1,-1\right\}\)