Question

解方程组 （x+y）（x+y-1）=56 （x-y）（x-y-1）=12

Answer 1

（x+y）（x+y-1）=56

(x+y)^2-(x+y)-56=0

(x+y-8)(x+y+7)=0

x+y=8 x+y=-7

（x-y）（x-y-1）=12

(x-y)^2-(x-y)-12=0

(x-y-4)(x-y+3)=0

x-y=3 x-y=-3

解得：

x = 6,y=2

x= -(3/2),y = -(11/2)

x= 5/2,y = 11/2

x =-5,y = -2