某刊一文阐述了构造法证明不等式的九个模型,笔者深受启发,对其中作者介绍的构造函数模型进行了挖掘,着重对构造函数模型,利用函数的有关性质解决不等式问题进行了再研究,以供大家参考.例1[2]已知:实数x_1,x_2,…,x_n满足x_1+x_2+…+x_n=a(a>0)且x_1~2+x_2~2+…+x_n~2=a~2/n-1(N≥2,n∈N),求证:0≤x_i≤2a/n(i=1,2,…,n).分析有些不等式可以和函数建立直接联系,通过构造 A journal article elaborates nine models of constructing method to prove inequalities. The author is deeply inspired to excavate the constructor model introduced by the author. Emphasis is put on revising the constructor model and using the related properties of the function to solve inequalities. For example, it is known that the real numbers x_1, x_2, ..., x_n satisfy x_1 + x_2 + ... + x_n = a (a> 0) and x_1 ~ 2 + x_2 ~ 2 + ... + x_n ~ 2 = a ~ 2 / n-1 (N≥2, n∈N), verify that: 0≤x_i≤2a / n (i = 1,2, ..., n) .Analysis Some inequalities can be directly related to the function.