Question

Tìm các số nguyên x và y thỏa mãn x² + 2y² + 2xy = y + 2

Answer 1

\(\Leftrightarrow4x^2+8y^2+8xy-4y=8\)

\(\Leftrightarrow\left(2x+2y\right)^2+\left(2y-1\right)^2=9=9^2+0^2\)

Th1: \(\left\{{}\begin{matrix}2y-1=0\\2x+2y=\pm3\end{matrix}\right.\) (ktm)

TH2: \(\left\{{}\begin{matrix}2x+2y=0\\2y-1=\pm3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-2\\y=2\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\end{matrix}\right.\)