若x^2-2x+y^2+8y+17=0,则x= ,y=

问题描述:

若x^2-2x+y^2+8y+17=0,则x= ,y=

x^2-2x+y^2+8y+17=0
(x^2-2x+1)+(y^2+8y+16)=0
(x-1)^2+(y+4)^4=0
x=1,y=-4

x^2-2x+y^2+8y+17=0
(x^2-2x+1)-1+(y^2+8y+16)-16+17=0
(x-1)^2-1+(y+4)^2-16+17=0
(x-1)^2+(y+4)^2=0
(x-1)^2=0
(y+4)^2=0
x=1,y=-4