1引言1919年,Weitzenbock提出了如下不等式:~([1])定理1设a,b,c,S分别是△ABC的边长与面积,则a~2+b~2+c~2≥4S3~(1/2).1937年,Finsler和Hadwiger建立了一个更强的不等式如下:~([2])定理2设a,b,c,S分别是△ABC的边长与面积,则4S3~(1/2)+∑(a-b)~2≤a~2+b~2+c~2≤4S3~(1/2)+3∑(a-b)~2.近年来,对Weitzenbock,Finsler-Hadwiger不等式的研究精彩纷呈,文[4]也总结了一系列研究成果其中有 1 Introduction In 1919, Weitzenbock proposed the following inequality: Theorem 1 Let a, b, c and 2 be the length and area of ​​△ ABC, 4S3 ~ (1/2). In 1937, Finsler and Hadwiger established a stronger inequality as follows: Theorem 2 Let a, b, c and S denote the length and area of ​​△ ABC respectively. 4S3 ~ (1/2) + Σ (ab) ~ 2≤a ~ 2 + b ~ 2 + c ~ 2≤4S3 ~ (1/2) + 3Σ (ab) ~ 2. In recent years, weitzenbock, Finsler -Hadwiger inequality brilliant research, article [4] also summarizes a series of research results which