Difference between revisions of "2006 AIME A Problems/Problem 15"

 
 
(11 intermediate revisions by 6 users not shown)
Line 1: Line 1:
== Problem ==
+
#REDIRECT [[2006 AIME I Problems/Problem 15]]
Given that <math> x, y, </math> and <math>z</math> are real numbers that satisfy:
 
 
 
<center><math> x = \sqrt{y^2-\frac{1}{16}}+\sqrt{z^2-\frac{1}{16}} </math> </center>
 
<center><math> y = \sqrt{z^2-\frac{1}{25}}+\sqrt{x^2-\frac{1}{25}} </math></center>
 
<center><math> z = \sqrt{x^2 - \frac 1{36}}+\sqrt{y^2-\frac 1{36}}</math></center>
 
 
 
and that <math> x+y+z = \frac{m}{\sqrt{n}}, </math> where <math> m </math> and <math> n </math> are positive integers and <math> n </math> is not divisible by the square of any prime, find <math> m+n.</math>
 
 
 
== Solution ==
 
 
 
== See also ==
 
*[[2006 AIME II Problems]]
 

Latest revision as of 21:36, 31 May 2009