Raising The Power of \(\alpha\)

Algebra Level 4

If \(\alpha\) is a real root of the equation
\[x^{5} - x^{3} + x- 2 = 0\]
Evaluate \(\lfloor {\alpha}^6 \rfloor\)

Details And Assumptions

\(\lfloor n \rfloor\) denotes the greatest integer less than or equal to \(n\).

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