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Indian Mathematical Olympiad 1990 - Problem 5

Source:

August 16, 2009
searchinequalitiestriangle inequalityalgebra proposedalgebralimitindia

Problem Statement

Let a a, b b, c c denote the sides of a triangle. Show that the quantity \frac{a}{b\plus{}c}\plus{}\frac{b}{c\plus{}a}\plus{}\frac{c}{a\plus{}b} must lie between the limits 3/2 3/2 and 2. Can equality hold at either limits?
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