Art of Problem Solving
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

2013 AMC 12A Problems/Problem 8

Revision as of 21:26, 6 February 2013 by Epicwisdom (talk | contribs) (Created page with "<math> x+\tfrac{2}{x}= y+\tfrac{2}{y} </math> Since <math>x\not=y</math>, we may assume that <math>x=\frac{2}{y}</math> and/or, equivalently, <math>y=\frac{2}{x}</math>. Cross ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

$x+\tfrac{2}{x}= y+\tfrac{2}{y}$

Since $x\not=y$, we may assume that $x=\frac{2}{y}$ and/or, equivalently, $y=\frac{2}{x}$.

Cross multiply in either equation, giving us $xy=2$.

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2013_AMC_12A_Problems/Problem_8&oldid=50727"