ĐKXĐ: \(\left\{{}\begin{matrix}2x-y>0\\x+y\ne0\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{4}{\sqrt{2x-y}}-\dfrac{21}{x+y}=\dfrac{1}{2}\\\dfrac{3}{\sqrt{2x-y}}+\dfrac{7-x-y}{x+y}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{\sqrt{2x-y}}-\dfrac{21}{x+y}=\dfrac{1}{2}\\\dfrac{3}{\sqrt{2x-y}}+\dfrac{7}{x+y}-1=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{\sqrt{2x-y}}-\dfrac{21}{x+y}=\dfrac{1}{2}\\\dfrac{3}{\sqrt{2x-y}}+\dfrac{7}{x+y}=2\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{2x-y}}=u>0\\\dfrac{1}{x+y}=v\end{matrix}\right.\) hệ trở thành:
\(\left\{{}\begin{matrix}4u-21v=\dfrac{1}{2}\\3u+7v=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}4u-21v=\dfrac{1}{2}\\9u+21v=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}13u=\dfrac{13}{2}\\9u+21v=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}u=\dfrac{1}{2}\\v=\dfrac{1}{14}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{\sqrt{2x-y}}=\dfrac{1}{2}\\\dfrac{1}{x+y}=\dfrac{1}{14}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}2x-y=4\\x+y=14\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=18\\x+y=14\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=8\end{matrix}\right.\)
