ReplaceAll[{α^2 + β^2, α^3 + β^3}, {α -> (1 - Sqrt[13])/3, β -> (1 + Sqrt[13])/3}]ReplaceAll[{α^2 + β^2, α^3 + β^3}, {α -> (1 - Sqrt[13])/3, β -> (1 + Sqrt[13])/3}]

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