Question

Tìm x; y nguyên, biết:

a) 2xy - 8x - y= -17

b) 5xy - 5x + y= 5

c) 2xy + x - 6y= 14

Answer 1

2xy - 8x - y = 17

=> 2x[y - 1] - y = 17

=> 2x[y - 1] - y + 1= 18

=> 2x[y - 1] - [y - 1] = 18

=> [2x - 1][y-1] = 18

Mà 2x - 1 lẻ nên 2x - 1 \(\in\left\{-9;-3;-1;1;3;9\right\}\)

Ta có:

2x-1	-9	-3	-1	1	3	9
y-1	-2	-6	-18	18	6	2
2x	-8	-2	0	2	4	10
x	-4	-1	0	1	2	5
y	-1	-5	-17	19	7	3

Vậy; .........

Answer 2

5xy - 5x + y = 5

=> 5x[y - 1] + y = 5

=> 5x[y-1] + y - 1 = 4

=> 5x[y-1] + [y-1] = 4

=> [5x - 1][y-1] = 4

Ta có:

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

Vậy:.........

Answer 3

2xy + x - 6y = 14

=> 2xy - 6y + x = 14

=> 2y[x - 3] + x = 14

=> 2y[x-3] + x-3 = 11

=> 2y[x-3] + [x-3] = 11

=> [2y - 1][x-3] = 11

Ta có:

2y-1	1	11	-1	-11
x-3	11	1	-11	-1
2y	2	12	0	-10
y	1	6	0	-5
x	14	4	-8	2

Vậy:...........