探究多变量不等式的证明  

Exploring the Proof of Multivariate Inequalities

作　　者：聂思兵 魏齐[1] 秦靖玻 李晓琪 李张世佳 黄黎明[1] 

机构地区：[1]内江职业技术学院通识与公共服务学院,四川 内江

出　　处：《应用数学进展》2024年第7期3554-3569,共16页Advances in Applied Mathematics

摘　　要：多变量问题如何消元,构造合适的一元函数是难点,根据特点构造合适的函数体现了学生对美学的认识,创新性。消元法中的整体换元法:若两个变量存在确定的关系,可以利用其中一个变量替换另一个变量,直接消元,将两个变量转化为一个变量。若两个变量不存在确定的关系,有时可以将两个变量之间的关系看成一个整体(比如t=x1x2,t=x1−x2)等策略,将两个变量划归为一个变量整体换元,化为一元不等式。How to eliminate variables in multivariate problems and construct appropriate univariate functions are difficult points. Constructing appropriate functions according to characteristics reflects students’ understanding of aesthetics and innovation. The overall substitution method in the elimination method: If there is a definite relationship between two variables, one variable can be used to replace the other variable, directly eliminate the variables, and transform the two variables into one variable. If there is no definite relationship between the two variables, sometimes the relationship between the two variables can be regarded as a whole (such ast=x1x2,t=x1−x2) and other strategies to classify the two variables as one variable and replace the variables as a whole, and transform them into a univariate inequality.

关 键 词：多变量不等式 消元法 数学核心素养 

分 类 号：G63[文化科学—教育学]