Đặt \(\left\{{}\begin{matrix}\sqrt{x}=a\ge0\\\sqrt{y}=b\ge0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=10\\\sqrt{a^2+6}+\sqrt{b^2+6}=14\end{matrix}\right.\)
\(\Rightarrow\sqrt{a^2+6}+\sqrt{\left(10-a\right)^2+6}=14\)
\(\Leftrightarrow\sqrt{a^2-20a+106}=14-\sqrt{a^2+6}\) (\(a\le\sqrt{190}\))
\(\Leftrightarrow a^2-20a+106=202-28\sqrt{a^2+6}+a^2\)
\(\Leftrightarrow7\sqrt{a^2+6}=5a+24\)
\(\Leftrightarrow49\left(a^2+6\right)=\left(5a+24\right)^2\)
\(\Leftrightarrow4a^2-40a-47=0\)
\(\Leftrightarrow...\)
