Đặt \(\left(\sqrt[3]{x};\sqrt[3]{y}\right)=\left(a;b\right)\)
\(\Rightarrow\left\{{}\begin{matrix}2\left(a^3+b^3\right)=3a^2b+3ab^2\\a+b=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\left(a^3+b^3\right)=\left(a+b\right)^3\\a+b=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\left(a+b\right)^3-9ab\left(a+b\right)=\left(a+b\right)^3\\a+b=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=6\\ab=8\end{matrix}\right.\) \(\Rightarrow\left(a;b\right)=\left(2;4\right);\left(4;2\right)\)
\(\Rightarrow\left(x;y\right)\)
