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Inequality with variables between 1/2 and 1

Source: Romanian NMO 2006, Grade 8, Problem 4

April 18, 2006
inequalitiescalculusderivativefunctiongeometrytrigonometryvector

Problem Statement

Let a,b,c∈[12,1]a,b,c \in \left[ \frac 12, 1 \right]. Prove that 2≤a+b1+c+b+c1+a+c+a1+b≤3. 2 \leq \frac{ a+b}{1+c} + \frac{ b+c}{1+a} + \frac{ c+a}{1+b} \leq 3 . selected by Mircea Lascu
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