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a/b + c/d for fixed n

Source: China TST 1993, problem 2

June 27, 2005
quadraticsfunctionalgebra unsolvedalgebrainequalities

Problem Statement

Let n≥2,n∈Nn \geq 2, n \in \mathbb{N}, a,b,c,d∈Na,b,c,d \in \mathbb{N}, ab+cd<1\frac{a}{b} + \frac{c}{d} < 1 and a+c≤n,a + c \leq n, find the maximum value of ab+cd\frac{a}{b} + \frac{c}{d} for fixed n.n.
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