解:x^+y^-10x+6y+34=0
x^-10x+25+y^+6y+9=0
(x-5)^+(y+3)^=0
( x-5)^=0 x-5=0 x=5
(y+3)^=0 y+3=0 y=-3
X^2+Y^2-10X+6Y+34=0
(X-5)^2+(Y+3)^2=0
(X-5)^2=0 X=5 X^2=25
(Y+3)^2=0 Y=-3 Y^2=9
x^2+y^2-10x+6y+34
=x^2-10x+25+y^2+6y+9
=(x-5)^2+(y+3)^2=0
所以x=5,y=-3
x^2=25,y^2=9
X=2,y=2