Question

已知xy为实数,且满足2x^2+4xy+4y^2+8x+12y+10=0,试求x+y的值

Answer 1

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