The cubic equation x^3 + kx + 1 = 0, where k is a constant, has roots α, β and γ. For each positive integer n, Sn = αn+βn+γn.
i/ State the value of S1 and express S2 in terms of k.
ii/ Show that for all n, Sn+3 + kSn+1 + Sn = 0
iii/ Hence, or otherwise, express α4+β4+γ4 in terms of k.
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