\(< =>x^3-x=0< =>x\left(x^2-1\right)=0< =>\left[{}\begin{matrix}x=0\\x^2-1=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
\(x^3=x\)
\(x^3-x=0\)
\(x\cdot\left(x+1\right)\cdot\left(x-1\right)=0\)
`=>`\(\left[{}\begin{matrix}x=0\\x+1=0\\x-1=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=0\\x=-1\\x=1\end{matrix}\right.\)
`=>`\(x\in\left\{0;-1;1\right\}\)
\(x^3=x\)
\(\Leftrightarrow x^3-x=0\)
\(\Leftrightarrow x\left(x^2-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm1\end{matrix}\right.\)
\(x^3=x\\ \Leftrightarrow x^3-x=0\\ \Leftrightarrow x\left(x^2-1\right)=0\\ \Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=1\end{matrix}\right.\)
