Difference between revisions of "2011 AIME II Problems/Problem 9"
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| − | Let <math>x_1, x_2, ... , x_6</math> be nonnegaative real numbers such that <math>x_1 +x_2 +x_3 +x_4 +x_5 +x_6 =1</math>, and <math>x_1 x_3 x_5 +x_2 x_4 x_6 \le \frac{1}{540}</math>. Let p and q be positive relatively prime integers such that \frac{p}{q} is the maximum possible value of | + | Let <math>x_1, x_2, ... , x_6</math> be nonnegaative real numbers such that <math>x_1 +x_2 +x_3 +x_4 +x_5 +x_6 =1</math>, and <math>x_1 x_3 x_5 +x_2 x_4 x_6 \le \frac{1}{540}</math>. Let p and q be positive relatively prime integers such that <math>\frac{p}{q}</math> is the maximum possible value of |
<math>x_1 x_2 x_3 + x_2 x_3 x_4 +x_3 x_4 x_5 +x_4 x_5 x_6 +x_5 x_6 x_1 +x_6 x_1 x_2</math>. Find p+q. | <math>x_1 x_2 x_3 + x_2 x_3 x_4 +x_3 x_4 x_5 +x_4 x_5 x_6 +x_5 x_6 x_1 +x_6 x_1 x_2</math>. Find p+q. | ||
Revision as of 18:14, 31 March 2011
Let 
be nonnegaative real numbers such that 
, and 
. Let p and q be positive relatively prime integers such that 
is the maximum possible value of
. Find p+q.
