Question

Tìm x, biết: 

x³ + 3x² + 3x =0

Mn giúp mik nhen^^

Answer 1

\(x^3+3x^2+3x=0\\ \Leftrightarrow x\left(x^2+3x+3\right)=0\\ \Leftrightarrow x=0\left(x^2+3x+3=x^2+3x+\dfrac{9}{4}=\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}>0\right)\)

Answer 2

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

\(\Rightarrow x\left(x^2+3x+3\right)=0\)

Mà: \(x^2+3x+3>0\)

=> x = 0

Answer 3

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

\(\Leftrightarrow x\left(x^2+3x+3\right)=0\)

mà \(x^2+3x+3=\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0\forall x\)

\(\Rightarrow x=0\)

 

Answer 4

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

\(\Leftrightarrow x\left(x^2+3x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+3x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{3}{4}=0\end{matrix}\right.\)

\(\Leftrightarrow x=0\)