# 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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