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 $n$ .

Raising The Power of α\alphaα