Question

Tim cặp số nghuyên x,y thỏa mãn:

a)5xy+5x+3y=-16

b)3x+7=y(x+2)

Answer 1

a) 5xy + 5x + 3y = -16

=> 5xy + 5x + 3y + 3 - 3 = -16

=> 5x(y + 1 ) + 3 ( y + 1 ) - 3 = -16

=> ( 5x + 3 ) ( y + 1 ) - 3 = - 16

=> ( 5x + 3 ) ( y + 1 ) = -13

Ta có bảng :

5x + 3	-13	1	-1	13
y + 1	1	-13	13	-1

=> 

x				2
y	0	-14	12	-2

Do x, y E Z => x = 2; y = -2

b) 3x + 7 = y( x + 2)

=> 3x + 7 = xy + 2y

=> 3x + 7 - xy - 2y = 0

=> 3x - xy + 1 + 6 - 2y = 0

=> x ( 3 - y ) + 1 + 2 ( 3 - y ) = 0

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

Ta có bảng :

x + 2	1	-1
3 - y	-1	1

 

=>

x	-1	-3
y	4	2

 

Vậy, x = -1; y = 4

hoặc x = -3 ; y =2