Question

Giải hệ phương trình \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}=1\\\sqrt[3]{x}+\sqrt[3]{y}=5\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(x;y\ge0\)

\(\sqrt{x}+\sqrt{y}=1\Rightarrow\left\{{}\begin{matrix}\sqrt{x}=1-\sqrt{y}\le1\\\sqrt{y}=1-\sqrt{x}\le1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\le1\\y\le1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\sqrt[3]{x}\le1\\\sqrt[3]{y}\le1\end{matrix}\right.\) \(\Rightarrow\sqrt[3]{x}+\sqrt[3]{y}< 5\) \(\Rightarrow\) hệ đã cho vô nghiệm