Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2025 SSMO Accuracy Round Problems/Problem 4

Revision as of 11:26, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>a,</math> <math>b,</math> and <math>c</math> be the roots of the polynomial <math>x^3+4x^2-3x-4</math>. Suppose that <cmath>\left|\frac{a}{b+c}+\frac{b...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $a,$ $b,$ and $c$ be the roots of the polynomial $x^3+4x^2-3x-4$. Suppose that \[\left|\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\right|=\frac{m}{n},\] for relatively prime positive integers $m$ and $n$. Find $m+n$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_SSMO_Accuracy_Round_Problems/Problem_4&oldid=260042"