X^2 + Y^2 -2X + 4Y = 20.(1)(X-Y)^2 + 6X - 6Y + 8 =0(X-Y)^2 + 6X - 6Y + 8 =0(x-y)^2+6(x-y)+8=0(x-y+4）（x-y+2)=0x-y=-4,y=x+4或x-y=-2.y=x+2将y=x+4和y=x+2分别代入方程（1）x^2-2x+(x+4)^2+4(x+4)=202x^2+10x+12=0x^2+5x+6=0(x+2)(x+3)x=-2或x=-3y=x+4=2或y=x+4=1x^2-2x+(x+2)^2+4(x+2)=202x^2+6x-8=0x^2+3x-4=0(x+4)(x-1)=0x=-4或x=1y=x+2=-2或y=x+2=3解得：x=-2,y=2或x=-3,y=1或x=-4,y=-2或x=1,y=3