已知xy为实数,且满足2x^2+4xy+4y^2+8x+12y+10=0,试求x+y的值
问题描述：
已知xy为实数,且满足2x^2+4xy+4y^2+8x+12y+10=0,试求x+y的值
如题.
答
由2x^2+4xy+4y^2+8x+12y+10=0得
x^2+2xy+2y^2+4x+6y+5=0
x^2+2(y+2)x+(y+2)^2-(y+2)^2+2y^2+6y+5=0
(x+y+2)^2+(y+1)^2=0
于是x+y+2=0 y+1=0
故x+y=-2