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Difference between revisions of "2024 AMC 8 Problems/Problem 10"

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==Solution 1==
 
==Solution 1==
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(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>.
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(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 12:33, 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

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