Question

已知a＞b＞c＞d 求证 1/（a-b)+1/(b-c)+1/(c-d)≥9/(a-d)

Answer 1

a-d=a-b+b-c+c-d

(b-c)/(a-b)+(c-d)/(a-b)+(a-b)/(b-c)+(c-d)/(b-c)+(a-b)/(c-d)+(b-c)/(c-d)+3>=9

再用均值不等式两两配对,等号成立条件是a-b=b-c=c-d