2015 AIME II Problems/Problem 8: Difference between revisions
Create Page |
m Add Solution Section |
||
| Line 1: | Line 1: | ||
==Problem | ==Problem== | ||
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>. | ||
==Solution== | |||
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 
.
