Difference between revisions of "2011 AIME II Problems/Problem 8"
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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}) | 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. | |
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Solution: | Solution: | ||
Revision as of 17:04, 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 iz_{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:
