已知X,Y为实数,且满足2X^2+4XY+4Y^2+8X+12Y+10=0,求x+y的值.
问题描述：
已知X,Y为实数,且满足2X^2+4XY+4Y^2+8X+12Y+10=0,求x+y的值.
答
2X^2+4XY+4Y^2+8X+12Y+10
=2(x+y)^2+2Y^2+8x+12y+10
=2(x+y)^2+8(x+y)+8+[2Y^2+4y+2]
=2[(x+y)+2]^2+2(y+1)^2=0
2[(x+y)+2]^2>=0
2(y+1)^2>=0
所以(x+y)+2＝0,且y+1＝0
所以x+y＝-2