If α and β are two of the roots of x^3 - x + 1 = 0, show that αβ is a root of x^3 + x^2 - 1 = 0. [Hint: Let x^3 - x + 1 = (x-α)(x-β)(x-γ)] [Hint #2: Show that: (αβ)^3 + (αβ)^2 - 1 = 0] How do I solve this?
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