Question

Giải phương trình sau:

\(\sqrt[3]{x^3+2x^2}=x+2\)

Answer 1

⇔ $x^{2}.(x+2)=(x+2)^{3}$

⇔$4(x+1)(x+2)=0$

→$x=-1 hoặc x=-2$

Answer 2

P/t \(\Leftrightarrow\sqrt[3]{x^2\left(x+2\right)}=x+2\)  

\(\Leftrightarrow\left(x+2\right)\left(\sqrt[3]{x^2}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\pm1\end{matrix}\right.\)

Answer 3

Lời giải:
ĐKXĐ: $x\in\mathbb{R}$

PT $\Leftrightarrow x^3+2x^2=(x+2)^3$

$\Leftrightarrow x^2(x+2)-(x+2)^3=0$

$\Leftrightarrow (x+2)[x^2-(x+2)^2]=0$

$\Leftrightarrow (x+2)(x-x-2)(x+x+2)=0$

$\Leftrightarrow (x+2)(-2).2(x+1)=0$

$\Leftrightarrow (x+2)(x+1)=0$

$\Leftrightarrow x+2=0$ hoặc $x+1=0$

$\Leftrightarrow x=-2$ hoặc $x=-1$