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a/c+c/b \ge 4a/(a + b) for a,b,c>0

Source: Austria Beginners' Competition 2018 p1

February 24, 2020

inequalitiesalgebra

Problem Statement

Let

a, b

and

c

denote positive real numbers. Prove that

\frac{a}{c}+\frac{c}{b}\ge \frac{4a}{a + b}

. When does equality hold?
(Walther Janous)

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