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Determine the range of X_0

Source: IMO Shortlist 1989, Problem 26, ILL 84

September 18, 2008
maximizationminimizationoptimizationalgebracalculusIMO Shortlist

Problem Statement

Let n \in \mathbb{Z}^\plus{} and let a,b∈R. a, b \in \mathbb{R}. Determine the range of x0 x_0 for which \sum^n_{i\equal{}0} x_i \equal{} a \text{ and } \sum^n_{i\equal{}0} x^2_i \equal{} b, where x0,x1,…,xn x_0, x_1, \ldots , x_n are real variables.
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