∵a>b>0,
∴2a＞a+b,a+b＞2b,ab＞b^2,a^2＞ab
∴a＞(a+b)/2＞b,a＞√ab＞b,
有a+b/2＞√ab
则a＞(a+b)/2＞√ab＞b
∴M∩N=(√ab,(a+b)/2)