1

Part of 2018 Austria Beginners' Competition

Problems(1)

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

Source: Austria Beginners' Competition 2018 p1

a, b

c

denote positive real numbers. Prove that

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

. When does equality hold?
(Walther Janous)

inequalitiesalgebra