Difference between revisions of "2006 AIME I Problems/Problem 15"
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== Problem == | == Problem == | ||
| − | Given that | + | |
| + | 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 == | == Solution == | ||
Revision as of 15:51, 25 September 2007
Problem
Given that 
and 
are real numbers that satisfy:
and that 
where 
and 
are positive integers and is not divisible by the square of any prime, find 
Solution
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See also
| 2006 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
