2017 AMC 10A 第 5 题

Question

两个非零实数的和等于它们乘积的

4

倍。这两个数的倒数之和是多少？

The sum of two nonzero real numbers is

4

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

1

2

4

8

12

把两个数记为

x

和

y

。

Name the two numbers

x

and

y

将给定方程两边同时除以

xy

。

Divide the given equation by

xy

设两个数为

x

、

y

。题目给出

x + y = 4xy

。

因为两数非零，可以用它们的乘积作分母：

\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{x + y}{xy} = 4\text{。}

所以正确答案是 C。

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.

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