2024 AMC 8 Problems/Problem 10

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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2024 AMC 8 Problems/Problem 10

Problem

Solution 1