2006 AIME A Problems/Problem 15

Problem

Given that $x, y,$ and $z$ are real numbers that satisfy:

$x = \sqrt{y^2-\frac{1}{16}}+\sqrt{z^2-\frac{1}{16}}$ $y = \sqrt{z^2-\frac{1}{25}}+\sqrt{x^2-\frac{1}{25}}$ $z = \sqrt{x^2 - \frac 1{36}}+\sqrt{y^2-\frac 1{36}}$

and that $x+y+z = \frac{m}{\sqrt{n}},$ where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime, find $m+n.$

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2006 AIME A Problems/Problem 15

Problem

Solution

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