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Product(x_i)=1

Source: Romanian IMO Team Selection Test TST 1999, problem 4

February 24, 2005
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Problem Statement

Show that for all positive real numbers x1,x2,…,xnx_1,x_2,\ldots,x_n with product 1, the following inequality holds 1n−1+x1+1n−1+x2+⋯+1n−1+xn≤1. \frac 1{n-1+x_1 } +\frac 1{n-1+x_2} + \cdots + \frac 1{n-1+x_n} \leq 1.
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