【摘要】 在各国高中数学联赛及IMO等大型数学赛事中,经常出现一类轮换对称不等式的证明或求其取值范围,这类题形态简单优美,但是其证明或求解却难度极大,在有限的时间内解决赛题非常艰难.介绍一类轮换对称不等式,利用它构造的函数凹凸特征明显,进而巧用Jensen不等式取等号的条件来妙解这类轮换对称不等式.更多还原

【Abstract】 In the national high school math League and IMO and other large mathematics competitions,often prove a class of symmetric inequalities or the rotation range of this kind of problem,the simple form is beautiful,but the proof or solution are extremely difficult,the final problem is very bitter hard solution in finite time. This paper introduced a kind of rotation symmetric inequalities,using convex function feature structure it is obvious,then using the Jensen inequality an equality condition to better solutions for this class of rotation symmetric inequality.更多还原