2017 AMC 10A Problems/Problem 5

Problem

The sum of two nonzero real numbers is 4 times their product. What is the sum of the reciprocals of the two numbers?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 12$

Let the two real numbers be $x,y$ . We are given that

$x+y=4xy,$

and dividing both sides by $xy$ ,

$\frac{x}{xy}+\frac{y}{xy}=4$

$\frac{1}{y}+\frac{1}{x}=\boxed{4 (D)}.$

2017 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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