∵a＞0,b＞0
∴（a+b）/2-√ab
＝［（√a）²+（√b）²］/2-√ab
＝［（√a）²-2√ab+（√b）²］/2
＝（√a-√b）²/2≥0
∴（a+b）/2≥√ab