Question

tìm x

x³+3x²+3x+2=0

Answer 1

ta có : \(x^3+3x^2+3x+2=0\Leftrightarrow x^3+2x^2+x^2+2x+x+2=0\)

\(\)\(\Leftrightarrow x^2\left(x+2\right)+x\left(x+2\right)+\left(x+2\right)=0\Leftrightarrow\left(x+2\right)\left(x^2+x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x^2+x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x\in\varnothing\end{matrix}\right.\) vậy \(x=-2\)

Answer 2

Cách khác :

\(x^3+3x^2+3x+2=0\)

\(\Leftrightarrow x^3+3x^2+3x+1+1=0\)

\(\Leftrightarrow\left(x+1\right)^3=-1\)

\(\Leftrightarrow x+1=-1\)

\(\Leftrightarrow x=-2\)

Vậy \(x=-2\)