Question 1
For positive $a$, $b$, $c$, that satisfy the condition $ab + bc + ca = 3$, prove an inequality:
$$
\frac{1}{2a^3+1} + \frac{1}{2b^3+1} + \frac{1}{2c^3+1} \ge 1.
$$
$$
\frac{1}{2a^3+1} + \frac{1}{2b^3+1} + \frac{1}{2c^3+1} \ge 1.
$$
MathNet 2016-part-07 — 182 problems (EN–VI) Question 1
Math Olympiad Vault · MathNet 2016-part-07 — 182 problems (EN–VI)