设x、y满足10x2-16xy+8y2+6x-4y+1=0,则x-y=_.

问题描述:

设x、y满足10x2-16xy+8y2+6x-4y+1=0,则x-y=______.

由10x2-16xy+8y2+6x-4y+1=0,得
(9x2-12xy+4y2)+(6x-4y)+1+(4y2-4xy+x2)=0,
(3x-2y)2+2(3x-2y)+1+(2y-x)2=0,
(3x-2y+1)2+(2y-x)2=0,
∴3x-2y+1=0,2y-x=0,
解得x=-0.5,y=-0.25,
∴x-y=-0.25;
故答案为:-0.25.