在不等式的证明中,有两类条件对称不等式是常见的,一类是(以下称类型1):设xi>0(i=1,2,…,n,n≥2),且∑i=1nxi=s(s是常数,s>0,以下同),求证:∑i=1nf(xi)≤M(或≥M)(其中M是常数,f(xi)是关于xi的对称式,以下同);另一类是(以下称类型2):设xi>0(i=1,2,…,n,n≥2),且∏i=1nxi=s,求证:∑i=1nf(xi)≤M(或≥M).文献[1]通过举例比较系统地阐述了类型1和类型2这两 In the proof of inequality, there are two types of conditional symmetric inequalities are common, one is (hereinafter referred to as type 1): Let xi> 0 (i = 1,2, ..., n, n ≥ 2), and Σi = 1nxi = s (s is a constant, s> 0, the same below), verify: Σi = 1nf (xi) ≤M (or ≥M) (where M is a constant and f (xi) is a symmetry about xi, (Xi> 0 (i = 1,2, ..., n, n≥2), and Πi = 1nxi = s, verify that Σi = 1nf (xi ) ≤M (or≥M) .In literature [1], the two types 1 and 2