Difference between revisions of "2011 AIME II Problems/Problem 8"

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Problem:
 
Problem:
  
Let <math>z_{1}, z_{}2, ... , z_{12}</math> be the 12 zeros of the polynomial z^12-2^36. For each j, let w_{j }be one of z_{j} or ''i''z_{j}. Then the maximum possible value of the real part of (somebody who knows how please create in an equation) SUM j=1 to 12 (w_{j})
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Let <math>z_{1}, z_{2}, ... , z_{12}</math> be the 12 zeros of the polynomial z^12-2^36. For each j, let <math>w_{j }</math>be one of <math>z_{j}</math> or <math>''i''z_{j}</math>. Then the maximum possible value of the real part of (somebody who knows how please create in an equation) SUM j=1 to 12 (<math>w_{j}</math>)
 
can be written as m+root(n), where m and n are positive integers. Find m+n.
 
can be written as m+root(n), where m and n are positive integers. Find m+n.
  
 
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Solution:
 
Solution:

Revision as of 18:05, 31 March 2011

Problem:

Let $z_{1}, z_{2}, ... , z_{12}$ be the 12 zeros of the polynomial z^12-2^36. For each j, let $w_{j }$be one of $z_{j}$ or $''i''z_{j}$. Then the maximum possible value of the real part of (somebody who knows how please create in an equation) SUM j=1 to 12 ($w_{j}$) can be written as m+root(n), where m and n are positive integers. Find m+n.


Solution:

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