A Three-Term Minimum

★ 7/10functions Extrema Substitution AM-GM inequality

Problem

For $a, b \in [0, 1]$ , find the minimum value of

S(a, b) = \frac{a}{1+b} + \frac{b}{1+a} + (1-a)(1-b).

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, Substitution, AM-GM, inequality

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