一道高中数学会考题蕴含的多种解法与分析  

Multiple solutions and analysis of a math examination question in senior high school

作　　者：夏顺友 仲崇轶 王常春 陈治友[3] XIA Shun-you;ZHONG Chong-yi;WANG Chang-chun;CHEN Zhi-you(School of Mathematics and Big Data,Guizhou Education University,Guiyang 550018;Department of Mathematics,Zunyi Normal College,Zunyi 563006;College of Mathematics and Information Scienc,Guiyang University,Guiyang 550005,Guizhou,China)

机构地区：[1]贵州师范学院数学与大数据学院,贵州贵阳550018 [2]遵义师范学院数学学院,贵州遵义563006 [3]贵阳学院数学与信息科学学院,贵州贵阳550005

出　　处：《贵阳学院学报（自然科学版）》2022年第3期107-111,共5页Journal of Guiyang University：Natural Sciences

基　　金：国家自然科学基金(项目编号:71961003);贵州师范学院博士基金(项目编号:2018BS005,2021039);贵州省教育厅青年科技人才成长项目(黔教合KY[2022]301号)。

摘　　要：针对贵州省2021年12月高中数学会考题第43题,先给出其多种求解方法,如拉格朗日乘数法、判别式法、均值不等式法、柯西不等式法、梯度法等等,以及这些解法的分析,然后对该题蕴含的一般二次约束条件下的线性目标优化问题的解的存在性,以及多种一般求解方法进行论述。For Guizhou Province high school math examination questions in December 2021,43,gives its multiple solution method,such as Lagrange multiplier method,discriminant method,average inequality method,cauchy inequality method,gradient method and so on,as well as the solutions of the these analysis,then the problem of general quadratic constraints under the condition of the existence of the solution of linear target optimization problem,And a variety of general solution methods are discussed.

关 键 词：拉格朗日乘数法 判别式法 均值不等式法 柯西不等式法 梯度法 

分 类 号：O122.7[理学—数学]