\(\sqrt[3]{x^3+8}=x+2\\ \Rightarrow x^3+8=\left(x+2\right)^3\\ \Rightarrow x^3+8=x^3+6x^2+12x+8\\ \Rightarrow6x^2+12x=0\\ \Rightarrow6x\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
\(PT\Leftrightarrow\sqrt[3]{\left(x+2\right)\left(x^2-2x+4\right)}-\sqrt[3]{\left(x+2\right)^3}=0\\ \Leftrightarrow\sqrt[3]{x+2}\sqrt[3]{x^2-2x+4-x^2-4x-4}=0\\ \Leftrightarrow\sqrt[3]{x+2}\sqrt[3]{-6x}=0\\ \Leftrightarrow\left[{}\begin{matrix}x+2=0\\-6x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
