2004年3月第16届亚太地区数学奥林匹克竞赛第5题为证明:对任意正实数a,b,c,均有(a2+2)(b2+2)(c2+2)≥9(ab+bc+ca).文[1]对该题提供了一种证明方法,从证明来看,该题貌似简单,实际上却有难度,本文从该题的本质考虑,得到一个一般性的结论.引理设hi-1,(i=1,2,…,n),且hihj≥0,则ni The 5th issue of the 16th Asia-Pacific Regional Mathematical Olympiad in March 2004 was to prove that for any positive real numbers a, b, c, there are (a2+2)(b2+2)(c2+2)≥9(ab+) Bc+ca). The paper [1] provides a proof method for this question. From the point of view of proof, the title looks simple and actually has difficulty. This article considers the essence of the question and gets a general conclusion. Lemma set up hi-1, (i=1, 2, ..., n), and hihj ≥ 0, then ni