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第16届(2004年)亚太地区数学奥林匹克竞赛最后一题是一道不等式证明题:题1证明:对任意正实数a,b,c,均有(a2+2)(b2+2)(c2+2)≥9(ab+bc+ca).该赛题曾是公认的难题,常见的证明会很繁琐:文[1]首先采用降幂策略,利用柯西不等式把原不等式左边的六次多项式放缩为三次多项式,然后利用基本不等式继续放缩,最后作差分析,利用抽屉原理并经过复杂的计算得到了所要证的不等式;文[2]直
The last question of the 16th (2004) Mathematical Olympiad in Asia Pacific Region is an inequality Proof: Problem 1 Proof: For any positive real number a, b, c, we have (a2 + 2) (b2 + 2) (c2 + 2) ≥9 (ab + bc + ca). The title was recognized as a difficult problem. The common evidence can be cumbersome: the text [1] first uses the power-reduction strategy to use the Cauchy inequality to convert the left- Scaling to the third degree polynomial, and then use the basic inequality to continue scaling, the final difference analysis, the use of drawer principle and complicated calculations to obtain the required card inequality; [2] straight