已知X^2+Y^2+4X+6Y+13=0(X\Y为实数),则XY=_
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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=_](/uploads/image/z/512516-20-6.jpg?t=%E5%B7%B2%E7%9F%A5X%5E2%2BY%5E2%2B4X%2B6Y%2B13%3D0%28X%5CY%E4%B8%BA%E5%AE%9E%E6%95%B0%29%2C%E5%88%99XY%3D_)
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
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
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