Question 124
Prove that for positive real numbers $a, b$ and $c$ such that $a+b+c=1$ the inequality
$$
\frac{1}{b c+a+\frac{1}{a}}+\frac{1}{c a+b+\frac{1}{b}}+\frac{1}{a b+c+\frac{1}{c}} \leqslant \frac{27}{31}
$$
holds.
(Marko Radovanović with collaborators)
$$
\frac{1}{b c+a+\frac{1}{a}}+\frac{1}{c a+b+\frac{1}{b}}+\frac{1}{a b+c+\frac{1}{c}} \leqslant \frac{27}{31}
$$
holds.
(Marko Radovanović with collaborators)