若a>b>c 且x>y>z 如何证明ax+by+cz>ay+bz+cx?

题目

若a>b>c 且x>y>z 如何证明ax+by+cz>ay+bz+cx?

答案

ax+by+cz-ay-bz-cx
=a(x-y)+b(y-z)-c(x-z)
=a(x-y)+b(y-z)-c(x-y)-c(y-z)
=(a-c)(x-y)+(b-c)(y-z)
>0