Question

Tìm x, y thuộc Z thỏa mãn: x-y+2xy=7

Answer 1

\(2x\left(2y+1\right)-\left(2y+1\right)=13\)

\(\left(2y+1\right)\left(2x-1\right)=13\)

\(\left(I\right)\left\{{}\begin{matrix}2y+1=13\Rightarrow y=6\\2x-1=1\Rightarrow x=1\end{matrix}\right.\)

(II) \(\left\{{}\begin{matrix}2y+1=-13\Rightarrow y=-7\\2x-1=-1\Rightarrow x=0\end{matrix}\right.\)

\(\left(III\right)\left\{{}\begin{matrix}2y+1=1\Rightarrow y=0\\2x-1=13\Rightarrow x=7\end{matrix}\right.\)

\(\left(IV\right)\left\{{}\begin{matrix}2y+1=-1\Rightarrow y=-1\\2x-1=-13\Rightarrow x=-6\end{matrix}\right.\)

Kết luận:

(x,y):=(1,6);(0,-7); (7,0); (-6,-1)