# 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 \(\lfloor {\alpha}^6 \rfloor\)

\[x^{5} - x^{3} + x- 2 = 0\]

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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