A sleep into Mathematical Madness

Algebra Level 4

If a complex number \(\alpha\) satisfies the equation \( \alpha^3-\alpha^2-2\alpha+1=0,\) where \(\alpha=x+\frac{1}{x}\) for some complex number \(x\), then what is the value of the expression below? \[x^{64}-2x^{52}+3x^{43}+2x^{38}-2x^{29}+5x^{17}+5x^{10}-7x^7+7\]

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