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2 ( b/(a + b) + bc /(b + c)+ ca/(c+ a) )+ 1 >= 6(ab + bc + ca)

Source: 2015 Saudi Arabia GMO TST I p1

July 26, 2020
algebrainequalities

Problem Statement

Let a,b,ca, b, c be positive real numbers such that a+b+c=1a + b + c = 1. Prove that 2(aba+b+bcb+c+cac+a)+1≥6(ab+bc+ca)2 \left( \frac{ab}{a + b} +\frac{bc}{b + c} +\frac{ca}{c+ a}\right)+ 1 \ge 6(ab + bc + ca)
Trần Nam Dũng
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