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α6+β6+γ6+(αβ)3+(βγ)3+(αγ)3 \large\alpha^6 + \beta^6 + \gamma^6 + (\alpha\beta)^3 + (\beta\gamma)^3 + (\alpha\gamma)^3 α6+β6+γ6+(αβ)3+(βγ)3+(αγ)3
Let α,β\alpha, \betaα,β and γ \gammaγ be the zeroes of the polynomial x3−x−1x^3-x-1x3−x−1. Find the value of the expression above.
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