HKTST 2016

For discussing Olympiad Level Algebra (and Inequality) problems
Atonu Roy Chowdhury
Posts: 63
Joined: Fri Aug 05, 2016 7:57 pm
Let $a,b,c$ be positive real numbers satisfying $abc=1$. Determine the smallest possible value of
$$\frac{a^3+8}{a^3(b+c)}+\frac{b^3+8}{b^3(a+c)}+\frac{c^3+8}{c^3(b+a)}$$