若a,b,c∈R*,求证：(a)/(√b)＋(b)/(√c)＋(c)/(√a)≥√a＋√b＋√c

Question

若a,b,c∈R*,求证：(a)/(√b)＋(b)/(√c)＋(c)/(√a)≥√a＋√b＋√c

Answer 1

不妨设a >= b >= c,则1/√a <= 1/√b <= 1/√c,
所以 a/√b＋b/√c＋c/√a >= a/√a＋b/√b＋c/√c = √a＋√b＋√c （乱序和大于逆序和）