已x²+2x-y²+6y-8=0,且x+y≠2,求x-y

已x²+2x-y²+6y-8=0,且x+y≠2,求x-y
已x²+2x-y²+6y-8=0,且x+y≠2,求x-y

已x²+2x-y²+6y-8=0,且x+y≠2,求x-y
x²+2x-y²+6y-8=0
(x+1)²-(y-3)²=0
x+1=0
y-3=0
x=-1
y=3
x-y=-1-3=-4

x²+2x-y²+6y-8=0
x²+2x+1-y²+6y-9=0
(x+1)²-(y-3)²=0
(x+1+y-3)(x+1-y+3)=0
(x+y-2)(x-y+4)=0
则x+y=2或x-y=-4

（x+1)^2 -(y-3)^2=0
(x+1 +y-3)(x+1 -y+3)=0
(x+y-2)(x-y +4)=0
x+y 不等于2
只能x-y +4 =0
x-y =-4

x+1=!y-3 ! 可得x+1=y-3 即x-y=-4
或x+1=-（y-3）即x+y=2与题设矛盾，舍去
故x-y=-4

x^2+2x-y^2+6y-8=0
(x+1)^2-(y-3)^2=0
则:x+1=y-3或x+1+y-3=0
则:x-y=-4或x+y=2(舍)
所以:x-y=4