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Part of 2011 Kosovo Team Selection Test

Problems(1)

Cyclic inequality (KSV IMO TST Question 1)

Source:

4/25/2011
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} }
inequalitiesinequalities unsolved