Question

Giải hệ:

\(\left\{{}\begin{matrix}x^2+2y=xy+2x\\\sqrt{x+y}=xy-2\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x^2+2y=xy+2x\left(1\right)\\\sqrt{x+y}=xy-2\left(2\right)\end{matrix}\right.\)\(\left(đk:x\ge-y\right)\)

\(\left(1\right)\Leftrightarrow\left(x-2\right)\left(x-y\right)=0\Leftrightarrow\left[{}\begin{matrix}x=y\Rightarrow\sqrt{2y}=y^2-2\left(3\right)\\x=2\Rightarrow\left(2\right)\Leftrightarrow\sqrt{2+y}=2y-2\left(4\right)\end{matrix}\right.\)

\(giải\left(3\right)và\left(4\right)\Rightarrow x;y\)