Cubes of a cubic

Algebra Level 4

Let the roots of the cubic equation \( { x }^{ 3 }-3{ x }^{ 2 }+5x-7 \) be \(\alpha, \beta \quad and \gamma \) . Then find \(\alpha ^{ 3 }+\beta ^{ 3 }+\gamma ^{ 3 } \)

This problem is a part of my set The Best of Me

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