Cyclic inequality (KSV IMO TST Question 1)
Source:
April 25, 2011
inequalitiesinequalities unsolved
Problem Statement
Let 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}
}