\(\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\left(1\right)\\2\left(x+y\right)-3\sqrt{x+1}=-5\left(2\right)\end{matrix}\right.\) ( I )
Lấy (1) - (2), ta được :
\(\left(I\right)\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}+3\sqrt{x+1}=9\\2\left(x+y\right)+\sqrt{x+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}=\dfrac{9}{4}\\2\left(x+y\right)+\sqrt{x+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{65}{16}\\2\left(\dfrac{65}{16}+y\right)+\sqrt{\dfrac{65}{16}+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{65}{16}\\y=-\dfrac{51}{16}\end{matrix}\right.\)
Vậy HPT ( I) có nghiệm duy nhất ( x;y )= ( \(\dfrac{65}{16};-\dfrac{51}{16}\) )
