AoPSWiki

Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.

Personal tools

Search

Toolbox

1986 AIME Problems/Problem 1

From AoPSWiki

Problem

What is the sum of the solutions to the equation $\displaystyle \sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}$ ?

Solution

Let $y = \sqrt[4]{x}$ . Then we have $y(7 - y) = 12$ , or, by simplifying,

This means that $\sqrt[4]{x} = y = 3$ or $4$ .

Thus the sum of the possible solutions for $x$ is $4^4 + 3^4 = 337$ .

See also

1986 AIME (Problems • Resources)
Preceded by First Question	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/1986_AIME_Problems/Problem_1"

Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us