x^2+y^2-2x+2y+3
=x²-2x+1 +y²+2y+1 +1
=(x-1)²+(y+1)²+1
∵(x-1)²>=0
(y+1)²>=0
∴原式>0
∴x^2+y^2-2x+2y+3的值总为正数