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MathNet 2015-part-02 — 191 problems (EN–VI) Question 115

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 115

For positive real numbers $a$, $b$, $c$ the following holds:
$$ab + bc + ca = 16, \quad a \ge 3.$$
Find the smallest possible value of the expression $2a + b + c$. (Michal Rolínek)