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Cyclic inequality (KSV IMO TST Question 1)

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April 25, 2011
inequalitiesinequalities unsolved

Problem Statement

Let a,b,ca,b,c be real positive numbers. Prove that the following inequality holds:
{ \sum_{\rm cyc}\sqrt{5a^2+5c^2+8b^2\over 4ac}\ge 3\cdot \root 9 \of{8(a+b)^2(b+c)^2(c+a)^2\over (abc)^2} }