2017 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

The sum of two nonzero real numbers is

4

times their product. What is the sum of the reciprocals of the two numbers?

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Solution

Let

x

and

y

be the two numbers. We are given that

x + y = 4xy.

Note that

\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{x + y}{xy} = 4.

Thus, C is the correct answer.

Concepts: algebraic manipulation · fraction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.