A quartic equation, 2x 4 - x 3 - 6 = 0, has roots , , ,

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A quartic equation, 2x4 - x3 - 6 = 0, has roots α, β, γ, δ. Show that the quartic equation with roots α3, β3, γ3, δ3 is 8y4 - y3 - 18y2 - 108y - 216 = 0. Hence, find the values of S6 and S-3.

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