Difference between revisions of "2006 AIME A Problems/Problem 15"
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== See also == | == See also == | ||
*[[2006 AIME II Problems]] | *[[2006 AIME II Problems]] | ||
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+ | [[Category:Intermediate Algebra Problems]] |
Revision as of 10:40, 16 July 2006
Problem
Given that and
are real numbers that satisfy:
![$x = \sqrt{y^2-\frac{1}{16}}+\sqrt{z^2-\frac{1}{16}}$](http://latex.artofproblemsolving.com/4/8/2/482ec834e100a5c445119023117da55b0a08dae6.png)
![$y = \sqrt{z^2-\frac{1}{25}}+\sqrt{x^2-\frac{1}{25}}$](http://latex.artofproblemsolving.com/0/7/e/07e3a5bfe68da11f9902c4b34d8381e913e31859.png)
![$z = \sqrt{x^2 - \frac 1{36}}+\sqrt{y^2-\frac 1{36}}$](http://latex.artofproblemsolving.com/0/0/b/00b6096d5f7c9f1584a2efea64e687039b0c28ff.png)
and that where
and
are positive integers and
is not divisible by the square of any prime, find