|
|
| (10 intermediate revisions by 5 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]]
| |
| − | | |
| − | [[Category:Intermediate Algebra Problems]]
| |
