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inequality involving triangle

Source: Romanian Dristict Olympiad 2015, Grade VIII, Problem 1

September 25, 2018
inequalities

Problem Statement

If a,b,c a,b,c represent the lengths of the sides of a triangle, prove the inequality: 3≤∑cyca−a+b+c. 3\le\sum_{\text{cyc}}\sqrt{\frac{a}{-a+b+c}} .
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