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(x+y)(x^3+y^3)/(x^2+y^2)^2

Source: Junior Turkish Mathematical Olympiad 2011 P1

July 2, 2012
inequalitiesinequalities proposedalgebraTurkey

Problem Statement

Show that 1≤(x+y)(x3+y3)(x2+y2)2≤981 \leq \frac{(x+y)(x^3+y^3)}{(x^2+y^2)^2} \leq \frac98 holds for all positive real numbers x,yx,y.
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