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(s-c)/\sqrt{a}+(s-b)/\sqrt{c}+(s-a)/\sqrt{b}\ge (s-b)/\sqrt{a}+(s-c)/\sqrt{b}+

Source: Greece JBMO TST 2000 p4

June 17, 2019
geometrygeometric inequalityinequalities

Problem Statement

Let a,b,ca,b,c be sidelengths with a≥b≥ca\ge b\ge c and s≥a+1s\ge a+1 where ss be the semiperimeter of the triangle. Prove that s−ca+s−bc+s−ab≥s−ba+s−cb+s−ac \frac{s-c}{\sqrt{a}}+\frac{s-b}{\sqrt{c}}+\frac{s-a}{\sqrt{b}}\ge \frac{s-b}{\sqrt{a}}+\frac{s-c}{\sqrt{b}}+\frac{s-a}{\sqrt{c}}
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