x+y=x^2-xy+y^2的整数解要用判别式法的,

Question

x+y=x^2-xy+y^2的整数解
要用判别式法的,

Answer 1

可转化为[(x-y)^2]/2+[(x-1)^2]/2+[(y-1)^2]/2=1
x,y为整数,则(x-y)^2=0 (x-1)^2=1 (y-1)^2=1 x=y=2或x=y=0
或(x-y)^2=1 (x-1)^2=1 (y-1)^2=0 x=2,y=1 或x=0,y=1
或(x-y)^2=1 (x-1)^2=0 (y-1)^2=1 x=1,y=2 或x=1,y=0