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?

$1$

$2$

$4$

$8$

$12$

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

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.