2007 UNCO Math Contest II Problems/Problem 4

Problem

If $x$ is a primitive cube root of one (this means that $x^3 =1$ but $x \ne 1$ ) compute the value of $x^{2006}+\frac{1}{x^{2006}}+x^{2007}+\frac{1}{x^{2007}}.$

Solution

$\fbox{+1}$

Since $x^3=1$ , $x^{2006}=x^2$ , $x^{2007}=1$ , $x+\frac{1}{x}=-1$

2007 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2007 UNCO Math Contest II Problems/Problem 4

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