Question

Tìm các cặp số nguyên (x;y) thỏa mãn: x^2 - xy - y = 4

Answer 1

\(\Leftrightarrow\left(x^2-1\right)-\left(xy+y\right)=3\)

\(\Leftrightarrow\left(x+1\right)\left(x-1\right)-y\left(x+1\right)=3\)

\(\Leftrightarrow\left(x+1\right)\left(x-y-1\right)=3\)

Ta có bảng sau:

x+1	-3	-1	1	3
x-y-1	-1	-3	3	1
x	-4	-2	0	2
y	-4	0	-4	0

Vậy \(\left(x;y\right)=\left(-4;-4\right);\left(-2;0\right);\left(0;-4\right);\left(2;0\right)\)