若x2+y2+2x-6y+10=0,求xy的值

若x2+y2+2x-6y+10=0,求xy的值
若x2+y2+2x-6y+10=0,求xy的值

若x2+y2+2x-6y+10=0,求xy的值
x2+y2+2x-6y+10
=x2+2x+1+y2-6y+9
=(x+1)2+(y-3)2=0
所以x+1=0,y-3=0
所以x=-1,y=3
所以xy=-3

即(x+1)^2+(y-3)^2=0
所以只可能x+1=0,y-3=0
所以xy=-3

x2+y2+2x-6y+10
=x2+2x+1+y2-6y+9
=(x+1)2+(y-3)2=0
所以x+1=0,y-3=0
所以x=-1,y=3
所以xy=-3

x^2+2x+1+y^2-6y+9=0
(x+1)^2+(y-3)^2=0
x=-1,y=3
xy=-3

x2+y2+2x-6y+10=0
（x+1)^22+(y-3)^2=0
所以
x+1=0
y-3=0
所以
x=-1
y=3
xy=-3

已知等式左边配方后发现x=-1,y=3所以xy=-3