# An Inequality Made Up Of Greek Alphabets

Calculus Level 5

Let $$0<\alpha,\beta,\gamma<\frac{1}{2}$$ be real numbers with $$\alpha+\beta+\gamma=1.$$ The minimum value of $$\delta$$ which satisfies the inequality

$\alpha^3+\beta^3+\gamma^3+4\alpha\beta\gamma \leq \delta$

can be expressed in the form $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a+b$$.

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