关于“三次对称多项式x^(3)+y^(3)+z^(3)-3xyz的因式分解及其应用”的注记  

A note on“The factorization of the cubic symmetric polynomial x^(3)+y^(3)+z^(3)-3xyz and its application”

作　　者：高睿 徐行忠 廖军 刘合国 GAO Rui;XU Xingzhong;LIAO Jun;LIU Heguo(Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China;School of Science,Hainan University,Haikou 570228,China)

机构地区：[1]湖北大学数学与统计学学院,湖北武汉430062 [2]海南大学理学院,海南海口570228

出　　处：《湖北大学学报（自然科学版）》2023年第6期847-857,共11页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(12171142、11971155、12071117)资助。

摘　　要：文献[1-3]中从三次对称多项式x^(3)+y^(3)+z^(3)-3xyz的因式分解出发,给出这个分解在恒等式证明、代数式简化、三次方程求根等方面的直接应用.本研究是文献[1-3]的继续和深化,从不同的角度,用不同的证明把文献[1-3]中的不少结论推广到一般情形.In references[1-3],the factorization of the cubic symmetric polynomial x^(3)+y^(3)+z^(3)-3xyz had been studied.Some applications of this factorization in the proof of identities,the simplication of algebraic expressions and the solution of cubic equations had also been provided.In this paper,as the continuation and deepening of references[1-3],many conclusions of references[1-3]can be extended to general cases with different proofs from different angles.

关 键 词：对称多项式 基本不等式 一元三次方程 等幂和方程组 

分 类 号：O151.2[理学—数学]