| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2009 |
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| Session | June |
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| Topic | Roots of polynomials |
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1 The equation
$$x ^ { 4 } - x ^ { 3 } - 1 = 0$$
has roots \(\alpha , \beta , \gamma , \delta\). By using the substitution \(y = x ^ { 3 }\), or by any other method, find the exact value of \(\alpha ^ { 6 } + \beta ^ { 6 } + \gamma ^ { 6 } + \delta ^ { 6 }\).