\(\left\{{}\begin{matrix}\dfrac{2}{\sqrt{x}+1}-\dfrac{1-x-y}{x+y}=\dfrac{22}{15}\\\dfrac{3}{\sqrt{x}+1}+\dfrac{5+x+y}{x+y}=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{\sqrt{x}+1}+\dfrac{x+y+1}{x+y}=\dfrac{22}{15}\\\dfrac{3}{\sqrt{x}+1}+\dfrac{5+x+y}{x+y}=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{\sqrt{x}+1}+1+\dfrac{1}{x+y}=\dfrac{22}{15}\\\dfrac{3}{\sqrt{x}+1}+1+\dfrac{5}{x+y}=3\end{matrix}\right.\)
\(ĐK:x\ge0;x+y\ne0\)
Đặt \(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x}+1}=a\\\dfrac{1}{x+y}=b\end{matrix}\right.\)
hpt trở thành:
\(\left\{{}\begin{matrix}2a+1+b=\dfrac{22}{15}\\3a+1+5b=3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2a+b=\dfrac{7}{15}\\3a+5b=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{1}{21}\\b=\dfrac{13}{35}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x}+1}=\dfrac{1}{21}\\\dfrac{1}{x+y}=\dfrac{13}{35}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x}+1=21\\13x+13y=35\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=400\\13.400+13y=35\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=400\\y=-\dfrac{5165}{13}\end{matrix}\right.\) \((tm)\)
Vậy nghiệm hpt \(\left(x;y\right)=\left(400;-\dfrac{5165}{13}\right)\)
