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Part of 2007 IMAR Test

Problems(1)

sup(S)

Source: IMAR Test 2007

1/27/2009
For real numbers xi>1,1≤i≤n,n≥2, x_{i}>1,1\leq i\leq n,n\geq 2, such that: \frac{x_{i}^2}{x_{i}\minus{}1}\geq S\equal{}\displaystyle\sum^n_{j\equal{}1}x_{j}, for all i\equal{}1,2\dots, n find, with proof, sup⁡S. \sup S.
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