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Prove this inequality from MTRP 2017

Source: MTRP 2017 Class 11-Short Answer Type Question: Problem 2 :-

May 26, 2020

inequalities

Problem Statement

Let

a

b

c

be positive reals such that

a+b+c=3

. Show that

\sqrt{\frac{a}{b+c}} + \sqrt{\frac{b}{c+a}} + \sqrt{\frac{c}{a+b}} \leq \frac{6}{\sqrt(a+b)(b+c)(c+a)}