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

1987 USAMO Problems/Problem 1

Revision as of 10:17, 20 December 2015 by Bassmaster (talk | contribs)

By expanding you get \[m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3\] From this the two $m^3$ cancel and you get: \[2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0\] You can divide by $n$ (nonzero). You get: \[2n^2+m+m^2n+3m^2-3mn=0\] You can now factor the equation into: \[2n^2+(m^2-3m)n+(3m^2+m)=0\]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1987_USAMO_Problems/Problem_1&oldid=73798"