Question

\(\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\\\left(x+y\right)-3\sqrt{x+1}=-5\end{matrix}\right.\)

Answer 1

ĐK: \(x\ge-1\)

Đặt \(a=x+y;b=\sqrt{x+1}\left(b\ge0\right)\)

\(\Leftrightarrow\left\{{}\begin{matrix}2a+b=4\\a-3b=-5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2a+b=4\\2a-6b=-10\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2a+b=4\\7b=14\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\end{matrix}\right.\)

\(b=2\Rightarrow\sqrt{x+1}=2\Leftrightarrow x=2^2-1=3\)

\(\Rightarrow y=a-x=1-3=-2\)

Vậy hpt có nghiệm (x,y) = (3;-2)