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2024 AMC 8 Problems/Problem 10: Difference between revisions

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What is the sum of the roots of <math>\frac{1}{x}</math> <math>+1=x</math>?
What is the sum of the roots of <math>\frac{1}{x}</math> <math>+1=x</math>?


A)0   B)-1   C)1   D)-2   E)2
 
<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ -1 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ -2 \qquad \textbf{(E)}\ 2</math>


==Solution 1==
==Solution 1==

Revision as of 11:44, 22 January 2024

Problem

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


$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ -1 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ -2 \qquad \textbf{(E)}\ 2$

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

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