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Weitzenberk不等式 :在△ ABC中 ,设BC=a,CA=b,AB=c,△表示△ABC的面积 .则a2 +b2 +c2≥ 4 3△ . (1)不等式 (1)有许多种加强 ,本文将给出不等式 (1)的一种半对称形式加强 .定理 在△ABC中 ,设 ma,ha 分别表示BC边上的中线和高 ,则nama(a2 +b2 +c2 )≥ 4 3△ . (2 )(2 )式当且
Weitzenberk inequality: In △ ABC, let BC = a, CA = b, AB = c, and △ denote the area of △ ABC. Then a2 + b2 + c2 ≥ 4 3 △ . (1) There are many kinds of inequality (1) In this paper, a semisymmetrical form enhancement of inequality (1) will be given. Theorem In △ABC, let ma,ha denote the midline and height on the BC side respectively, then nama(a2 +b2 +c2)≥4 3△ (2) When (2)