原文地址:爱尔兰数学奥林匹克不等式题及其证明大全(1988-2012)作者:sqing55 irish mathematical olympiads 1988 - 2012 i do love irish ineq ality problems very m ch. they always make me happy. -- epsilonist 2012证明1 (a)令 and ,要证 只要证 即证 , 亦即证 ,而 证明2 等价于 . 证明3  mviewtopic.php?f=52&t=&hilit=irish55 证明4(anzhenping) 2012证明1 由契比雪夫不等式及 得 , 故 .  mviewtopic.php?f=52&t=&hilit=irish55 证明2 证明3(天天向上 )证明4(熊昌进 ) 证明5(anzhenping ) 1988 证明 let so that and we have to prove which can be rewritten as (since this is obvio s for ) which is perfectly tr e on sing the am-gm ineq ality: 1989 证明(张云华)  证明(张云华) 1991 证明(张云华)  证明(张云华) 1998 (安振平) 证明2(张云华) 1998证明(张云华) 1999证明(张云华) 2000 (polskimisiek 2008) (karis 2008) 证明(张云华) 已知 是满足 的正数 , 证明: 证明(sqing)let , so 注 在相同的条件下,蒙古人s njee猜想 ,台湾人scaleye举反例否定,并说 亦不成立.2001 prove that for all positive integers the following ineq ality holds:  mviewtopic.php?f=51&p=#p 2001证明(张云华) 2002证明(张云华) 证明2 by am-gm, we have . now, consider , or , or . it is easy to see that is concave for ;