MathDB

2013-2014 Fall OMO #30

Source:

October 30, 2013

Online Math Opengeometryalgebrapolynomialnumber theoryrelatively primearea of a triangle

Problem Statement

Let

P(t) = t^3+27t^2+199t+432

. Suppose

a

b

c

, and

x

are distinct positive reals such that

P(-a)=P(-b)=P(-c)=0

, and

\sqrt{\frac{a+b+c}{x}} = \sqrt{\frac{b+c+x}{a}} + \sqrt{\frac{c+a+x}{b}} + \sqrt{\frac{a+b+x}{c}}.

x=\frac{m}{n}

for relatively prime positive integers

m

and

n

, compute

m+n

.
Proposed by Evan Chen