\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{xy}+\sqrt{y}=11+12\sqrt{13}\\x+y=134\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x}+1\right)\left(\sqrt{y}+1\right)=12+12\sqrt{13}\\x+y=134\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x}+1=a\\\sqrt{y}+1=b\end{matrix}\right.\) \(\left(a,b>0\right)\)
\(Hpt\Leftrightarrow\left\{{}\begin{matrix}ab=12+12\sqrt{13}\\a^2+b^2-2\left(a+b\right)+2=134\end{matrix}\right.\)
\(\Leftrightarrow a^2+b^2+2ab-2\left(a+b\right)+1=134+12+12\sqrt{13}-1\)
\(\Leftrightarrow\left(a+b\right)^2-2\left(a+b\right)+1=145+12\sqrt{13}\)
\(\Leftrightarrow\left(a+b-1\right)^2=145+12\sqrt{13}\)
\(\Leftrightarrow a+b=\sqrt{145+12\sqrt{13}}+1\)
\(Hpt\Leftrightarrow\left\{{}\begin{matrix}ab=12+12\sqrt{13}\\a+b=\sqrt{145+12\sqrt{13}}+1\end{matrix}\right.\)
Số xấu quá nên dừng tại đây :D
