Đặt \(\left\{{}\begin{matrix}\sqrt[3]{x+10}=a\\\sqrt[3]{17-x}=b\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a+b=3\\a^3+b^3=27\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}b=3-a\\a^3+b^3=27\end{matrix}\right.\)
\(\Rightarrow a^3+\left(3-a\right)^3-27=0\)
\(\Leftrightarrow9a^2-27a=0\Rightarrow\left[{}\begin{matrix}a=0\\a=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt[3]{x+10}=0\\\sqrt[3]{x+10}=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-10\\x=17\end{matrix}\right.\)
