Question

\(\left\{{}\begin{matrix}\sqrt[3]{x}+\sqrt[3]{y}=4\\xy=27\end{matrix}\right.\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt[3]{x}+\sqrt[3]{y}=4\\\sqrt[3]{xy}=3\end{matrix}\right.\)

Theo Viet đảo, \(\sqrt[3]{x}\) và \(\sqrt[3]{y}\) là nghiệm:

\(t^2-4t+3=0\Rightarrow\left[{}\begin{matrix}t=1\\t=3\end{matrix}\right.\)

\(\Leftrightarrow\left(\sqrt[3]{x};\sqrt[3]{y}\right)=\left(1;3\right);\left(3;1\right)\)

\(\Rightarrow\left(x;y\right)=\left(1;27\right);\left(27;1\right)\)