Question

[Linh Phương]

Tìm các cặp số nguyên (x, y) thỏa mãn x-3y+2xy=4

Answer 1

[Nguyễn Lê Phước Thịnh]

=>x(2y+1)-3y-1,5=2,5

=>(y+0,5)(2x-3)=2,5

=>(2y+1)(2x-3)=5

=>\(\left(2x-3;2y+1\right)\in\left\{\left(1;5\right);\left(5;1\right);\left(-1;-5\right);\left(-5;-1\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(2;2\right);\left(4;0\right);\left(1;-3\right);\left(-1;-1\right)\right\}\)

Answer 2

[Nguyễn Việt Lâm]

\(2xy+x-3y=4\)

\(\Leftrightarrow4xy+2x-6y=8\)

\(\Leftrightarrow4xy+2x-6y-3=5\)

\(\Leftrightarrow2x\left(2y+1\right)-3\left(2y+1\right)=5\)

\(\Leftrightarrow\left(2x-3\right)\left(2y+1\right)=5\)

2x-3	-5	-1	1	5
2y+1	-1	-5	5	1
x	-1	1	2	4
y	-1	-3	2	0

Vậy pt có các cặp nghiệm nguyên \(\left(x;y\right)=\left(-1;-1\right);\left(1;-3\right);\left(2;2\right);\left(4;0\right)\)