Difference between revisions of "2015 AIME II Problems/Problem 8"
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Let <math>a</math> and <math>b</math> be positive integers satisfying <math>\frac{ab+1}{a+b} < \frac{3}{2}</math>. The maximum possible value of <math>\frac{a^3b^3+1}{a^3+b^3}</math> is <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | Let <math>a</math> and <math>b</math> be positive integers satisfying <math>\frac{ab+1}{a+b} < \frac{3}{2}</math>. The maximum possible value of <math>\frac{a^3b^3+1}{a^3+b^3}</math> is <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | ||
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Revision as of 18:25, 26 March 2015
Problem
Let 
and 
be positive integers satisfying 
. The maximum possible value of 
is 
, where 
and 
are relatively prime positive integers. Find 
.
