A sleep into Mathematical Madness

Algebra Level 4

If a complex number α\alpha satisfies the equation α3α22α+1=0, \alpha^3-\alpha^2-2\alpha+1=0, where α=x+1x\alpha=x+\frac{1}{x} for some complex number xx, then what is the value of the expression below? x642x52+3x43+2x382x29+5x17+5x107x7+7x^{64}-2x^{52}+3x^{43}+2x^{38}-2x^{29}+5x^{17}+5x^{10}-7x^7+7

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