IMO Shortlist 1995 problem S2


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2. travnja 2012.
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Find the maximum value of x_{0} for which there exists a sequence x_{0},x_{1}\cdots ,x_{1995} of positive reals with x_{0} = x_{1995}, such that
x_{i - 1} + \frac {2}{x_{i - 1}} = 2x_{i} + \frac {1}{x_{i}},
for all i = 1,\cdots ,1995.
Izvor: Međunarodna matematička olimpijada, shortlist 1995