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FM June 2025 p11 q02
4116
The cubic equation \(x^3 + 2x + 1 = 0\) has roots \(\alpha, \beta, \gamma\).
- Find a cubic equation whose roots are \(\alpha^3 - 1, \beta^3 - 1, \gamma^3 - 1\).
- Find the value of \((\alpha^3 - 1)^2 + (\beta^3 - 1)^2 + (\gamma^3 - 1)^2\).
- Find the value of \((\alpha^3 - 1)^3 + (\beta^3 - 1)^3 + (\gamma^3 - 1)^3\).
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