Question

Tìm x,y\(\in Z\) biết:

\(\left(\sqrt{x}-1\right)\left(1+\sqrt{y}\right)=1\)

Answer 1

\(\left(\sqrt{x}-1\right)\left(1+\sqrt{y}\right)=1\left(x;y\ge0\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\sqrt{x}-1=1\\1+\sqrt{y}=1\end{matrix}\right.\\\left\{{}\begin{matrix}\sqrt{x}-1=-1\\1+\sqrt{y}=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=4\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}0\\\sqrt{y}=-2\left(l\right)\end{matrix}\right.\end{matrix}\right.\)

Vậy: \(x=4;y=0\)