Question

[Lê Anh]

Tìm các cặp số nguyên (x,y) thỏa mãn :

a) xy + 3x -y = 8

b) 2xy - 4x + y = 8

Answer 1

[Đặng Tú Phương]

a;\(xy+3x-y=8\)

\(\Rightarrow x\left(y+3\right)-\left(y+3\right)=8-3\)

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

\(\Rightarrow\left(x-1\right);\left(y+3\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét bảng 

x-1	1	-1	5	-5
y+3	5	-5	1	-1
x	2	0	6	-4
y	2	-8	-2	-4

Vậy..............................

b,\(2xy-4x+y=8\)

\(\Rightarrow x\left(2y-4\right)+y=8\)

\(\Rightarrow2x\left(2y-4\right)+\left(2y-4\right)=8-4\)

\(\Rightarrow\left(2x+1\right)\left(2y-4\right)=4\)

\(\Rightarrow\left(2x+1\right);\left(2y-4\right)\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

Xét bảng 

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

Vậy.....................................