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Simple inequality

Source: JBMO 2011 Shortlist A6

May 16, 2016
inequalitiesalgebraJBMO

Problem Statement

Let xi>1,∀i∈{1,2,3,…,2011}\displaystyle {x_i> 1, \forall i \in \left \{1, 2, 3, \ldots, 2011 \right \}}. Show that:x12x2−1+x22x3−1+x32x4−1+…+x20102x2011−1+x20112x1−1≥8044\displaystyle{\frac{x^2_1}{x_2-1}+\frac{x^2_2}{x_3-1}+\frac{x^2_3}{x_4-1}+\ldots+\frac{x^2_{2010}}{x_{2011}-1}+\frac{x^2_{2011}}{x_1-1}\geq 8044} When the equality holds?
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