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2021 April MIMC 10 Problems/Problem 12

Revision as of 17:18, 22 April 2021 by Cellsecret (talk | contribs) (Created page with "Given that <math>x^2-\frac{1}{x^2}=2</math>, what is <math>x^{16}-\frac{1}{x^{8}}+x^{8}-\frac{1}{x^{16}}</math>? <math>\textbf{(A)} ~1120 \qquad\textbf{(B)} ~1180 \qquad\text...")
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Given that $x^2-\frac{1}{x^2}=2$, what is $x^{16}-\frac{1}{x^{8}}+x^{8}-\frac{1}{x^{16}}$?

$\textbf{(A)} ~1120 \qquad\textbf{(B)} ~1180 \qquad\textbf{(C)} ~3780 \qquad\textbf{(D)} ~840\sqrt{2} \qquad\textbf{(E)} ~1260\sqrt{2}$

Solution

To be Released on April 26th.

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