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Romanian TST 1992

Source: Romanian TST 1992 - Day 4 - Problem 1

April 9, 2012
inequalitiesinequalities proposed

Problem Statement

Let x,yx, y be real numbers such that 1≤x2−xy+y2≤21\le x^2-xy+y^2\le2. Show that: a) 29≤x4+y4≤8\dfrac{2}{9}\le x^4+y^4\le 8; b) x2n+y2n≥23nx^{2n}+y^{2n}\ge\dfrac{2}{3^n}, for all n≥3n\ge3.
Laurențiu Panaitopol and Ioan Tomescu
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