The cubic equation x 3 - x + 3 = 0 has roots , , . a.

Question:

The cubic equation x3 - x + 3 = 0 has roots α, β, γ.

a. Using the relation Sn, = αn + βn + γn, or otherwise, find the value of S4.

b. By considering S1 and S4, determine the value of α3(β + γ) + β3(α + γ) + γ3(α + β).

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