已知X^2+Y^2+4X+6Y+13=0(X\Y为实数),则XY=_

已知X^2+Y^2+4X+6Y+13=0(X\Y为实数),则XY=_
已知X^2+Y^2+4X+6Y+13=0(X\Y为实数),则XY=_

已知X^2+Y^2+4X+6Y+13=0(X\Y为实数),则XY=_
x^2+y^2+4x+6y+13＝0
x^2 + y^2 + 4x + 6y + 4 + 9 ＝ 0
x^2 + 4x + 4 + y^2 + 6y + 9 ＝ 0
(x + 2)^2 + (y + 3)^2 ＝ 0
(∵(x + 2)^2 >= 0,(y + 3)^2 >= 0)
=> (x + 2)^2 = 0,(y + 3)^2 = 0
=> x + 2 = 0,y + 3 = 0
=> x = -2,y = -3

X²+Y²+4X+6Y+13=(x+2)²+(y+3)²=0
∴x=-2，y=-3
∴xy=6