MathNet 2020 — Math Olympiad Vault — Part 01 Question 126

Suppose positive real numbers $a$, $b$, and $c$ satisfy $a^2 + 4b^2 + 9c^2 = 4b + 12c - 2$. Find the minimum of $\frac{1}{a} + \frac{2}{b} + \frac{3}{c}$.