已知x²-3xy+4x=3,y²+xy-4y+7=0,则xy-1/2(x²+y²)的值为

问题描述:

已知x²-3xy+4x=3,y²+xy-4y+7=0,则xy-1/2(x²+y²)的值为

x²-3xy+4x=3,y²+xy-4y+7=0
相加得x²-2xy+y²+4(x-y)+4=0
(x-y)²+4(x-y)+4=0
(x-y+2)=0,得x-y=-2
xy-1/2(x²+y²)=-(1/2)(x-y)²=-(1/2)*4=-2