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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