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Let 0<α,β,γ<120<\alpha,\beta,\gamma<\frac{1}{2}0<α,β,γ<21 be real numbers with α+β+γ=1.\alpha+\beta+\gamma=1.α+β+γ=1. The minimum value of δ\deltaδ which satisfies the inequality
α3+β3+γ3+4αβγ≤δ\alpha^3+\beta^3+\gamma^3+4\alpha\beta\gamma \leq \deltaα3+β3+γ3+4αβγ≤δ
can be expressed in the form ab \frac{a}{b} ba, where aaa and bbb are positive coprime integers. Find a+ba+ba+b.
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