`#3107.101107`
`x^3 + 1 = x(x + 1)`
`=> x^3 + 1 - x(x + 1) = 0`
`=> x^3 + 1 - x^2 - x = 0`
`=> x^3 - x^2 - x + 1 = 0`
`=> x^2(x - 1) - (x - 1) = 0`
`=> (x^2 - 1)(x - 1) = 0`
`=> (x + 1)(x - 1)(x - 1) = 0`
`=> (x + 1)(x - 1)^2 = 0`
`=>`\(\left[{}\begin{matrix}x+1=0\\\left(x-1\right)^2=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=-1\\x-1=0\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)
Vậy, `x \in {-1; 1}.`
`x^3 + 1=x(x+1)`
`<=>(x+1)(x^2- x+1)-x(x+1)=0`
`<=>(x+1)[(x^2-x+1)-x)]=0`
`<=>(x+1)(x^2-x+1-x)=0`
`<=>(x+1)(x^2-2x+1)=0`
`<=>(x+1)(x-1)^2`
`<=>` \(\left[{}\begin{matrix}x+1=0\\\left(x-1\right)^2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\end{matrix}\right.\)
`<=>` \(\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)
Vậy `x=-1` hoặc `x=1`