证明:
(ax+by)(ay+bx)-xy
=xya^2+abx^2+aby^2+xyb^2-xy
=xy(a^2+2ab+b^2)-2abxy+abx^2+aby^2-xy
=xy(a+b)^2+ab(x^2-2xy+y^2)-xy 因为a+b=1
=xy+ab(x-y)^2-xy
=ab(x-y)^2 又因为:abxy都是正实数
则ab(x-y)^2>=0
即(ax+by)(ay+bx)-xy>=0
也就是(ax+by)(ay+bx)>=xy
证明:
(ax+by)(ay+bx)-xy
=xya^2+abx^2+aby^2+xyb^2-xy
=xy(a^2+2ab+b^2)-2abxy+abx^2+aby^2-xy
=xy(a+b)^2+ab(x^2-2xy+y^2)-xy 因为a+b=1
=xy+ab(x-y)^2-xy
=ab(x-y)^2 又因为:abxy都是正实数
则ab(x-y)^2>=0
即(ax+by)(ay+bx)-xy>=0
也就是(ax+by)(ay+bx)>=xy