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find the maximal value

Source: China south east mathematical Olympiad 2008 day2 problem 5

July 15, 2013
inequalitiesinequalities unsolved

Problem Statement

Let λ\lambda be a positive real number. Inequality ∣λxy+yz∣≤52|\lambda xy+yz|\le \dfrac{\sqrt5}{2} holds for arbitrary real numbers x,y,zx, y, z satisfying x2+y2+z2=1x^2+y^2+z^2=1. Find the maximal value of λ\lambda.
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