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Finding Max!

Source: Iran 3rd round 2013 - Algebra Exam - Problem 2

September 11, 2013
inequalities proposedinequalities

Problem Statement

Real numbers a1,a2,…,ana_1 , a_2 , \dots, a_n add up to zero. Find the maximum of a1x1+a2x2+⋯+anxna_1 x_1 + a_2 x_2 + \dots + a_n x_n in term of aia_i's, when xix_i's vary in real numbers such that (x1−x2)2+(x2−x3)2+⋯+(xn−1−xn)2≤1(x_1 - x_2)^2 + (x_2 - x_3)^2 + \dots + (x_{n-1} - x_n)^2 \leq 1. (15 points)
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