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

2024 AMC 8 Problems/Problem 10: Difference between revisions

← Older editNewer edit →
Multpi12 (talk | contribs)
editor
290 edits
Multpi12 (talk | contribs)
editor
290 edits
Line 5: Line 5:


==Solution 1==
==Solution 1==
(joke problem but decided to answer it)The answer is <math>/boxed {C}</math>. If you multiply the equation by x you get <math>1+x=x^2</math> . Now moving it to a quadratic you get <math>-x^2+x+1</math> . Using Vieta's <math>-b/a</math> is -<math>1/-1</math> which is <math>1</math>.
(joke problem but decided to answer it)The answer is <math>{C}</math>. If you multiply the equation by x you get <math>1+x=x^2</math> . Now moving it to a quadratic you get <math>-x^2+x+1</math> . Using Vieta's <math>-b/a</math> is -<math>1/-1</math> which is <math>1</math>.


-Multpi12
-Multpi12

Revision as of 11:33, 21 January 2024

Problem

What is the sum of the roots of $\frac{1}{x}$ $+1=x$?

A)0 B)-1 C)1 D)-2 E)2

Solution 1

(joke problem but decided to answer it)The answer is ${C}$. If you multiply the equation by x you get $1+x=x^2$ . Now moving it to a quadratic you get $-x^2+x+1$ . Using Vieta's $-b/a$ is -$1/-1$ which is $1$.

-Multpi12

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_AMC_8_Problems/Problem_10&oldid=211810"