Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
Question:
Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
Answer:
Let's think step by step.

user
20
Let $a$ and $b$ be real numbers such that $a > 2b > 0.$  Find the minimum value of
\[3a^3 \sqrt{3} + \frac{2}{ab - 2b^2}.\]
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