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MathNet 2015-part-04 — 191 problems (EN–VI) Question 72

Math Olympiad Vault · MathNet 2015-part-04 — 191 problems (EN–VI)

Question 72

Let $a$, $b$, $c$ be positive real numbers such that $a + b + c = 3$. Find the minimum value of the expression
$$
A = \frac{2 - a^3}{a} + \frac{2 - b^3}{b} + \frac{2 - c^3}{c}
$$