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Difference between revisions of "2013 AMC 12B Problems/Problem 24"

(Created page with "==Problem== Let <math>P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)</math>. What is the minimum perimeter among all the <math>8</math>-sided polygons i...")
 
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==Problem==
 
  
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Let <math>P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)</math>. What is the minimum perimeter among all the <math>8</math>-sided polygons in the complex plane whose vertices are precisely the zeros of <math>P(z)</math>?
 
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<math>\textbf{(A)}\ 4\sqrt{3} + 4 \qquad \textbf{(B)}\ 8\sqrt{2} \qquad \textbf{(C)}\  3\sqrt{2} + 3\sqrt{6} \qquad \textbf{(D)}\  4\sqrt{2} + 4\sqrt{3} \qquad \textbf{(E)}\  4\sqrt{3} + 6</math>
 

Revision as of 16:44, 22 February 2013

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