MathDB
Aime ii - 2006/15

Source:

March 27, 2006
AMCAIMEgeometryinequalitiesarea of a triangleHeron's formulaHi

Problem Statement

Given that xx, yy, and zz are real numbers that satisfy: x=y2−116+z2−116 x=\sqrt{y^2-\frac{1}{16}}+\sqrt{z^2-\frac{1}{16}} y=z2−125+x2−125 y=\sqrt{z^2-\frac{1}{25}}+\sqrt{x^2-\frac{1}{25}} z=x2−136+y2−136 z=\sqrt{x^2-\frac{1}{36}}+\sqrt{y^2-\frac{1}{36}} and that x+y+z=mnx+y+z=\frac{m}{\sqrt{n}}, where mm and nn are positive integers and nn is not divisible by the square of any prime, find m+nm+n.
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