若有理数X、Y满足x²-4x+y²+6y+13=0,求xy的值

若有理数X、Y满足x²-4x+y²+6y+13=0,求xy的值
若有理数X、Y满足x²-4x+y²+6y+13=0,求xy的值

若有理数X、Y满足x²-4x+y²+6y+13=0,求xy的值
x²-4x+y²+6y+13=0；
(x-2)²+(y+3)²=0;
x=2;y=-3;
xy=-6;

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

x²-4x+y²+6y+13=0
（x²-4x+4）+（y²+6y+9）=0
(x-2)²+(y+3)²=0
∴(x-2)²=0,(y+3)²=0
x-2=0, y+3=0
x=2, y=-3
∴xy=2×(-3)=-6

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