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inequality in n variables

Source: Romanian I TST 2007

April 13, 2007
inequalitiesinductionlogarithmscalculusderivativeinequalities proposed

Problem Statement

If a1a_{1}, a2a_{2}, …\ldots, an≥0a_{n}\geq 0 are such that a12+⋯+an2=1,a_{1}^{2}+\cdots+a_{n}^{2}=1, then find the maximum value of the product (1−a1)⋯(1−an)(1-a_{1})\cdots (1-a_{n}).
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