AMC12 2017 A

AMC12 2017 A · Q2

AMC12 2017 A · Q2. It mainly tests Linear equations, Manipulating equations.

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

两个非零实数的和是它们积的 4 倍。这两个数的倒数之和是多少？

(A) 1 1

(B) 2 2

(D) 8 8

(E) 12 12

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Let the two numbers be $x$ and $y$. Then $x+y=4xy$. Dividing this equation by $xy$ gives $\frac{1}{y}+\frac{1}{x}=4$. One such pair of numbers is $x=\frac{1}{3},\ y=1$.

答案（C）：设这两个数为 $x$ 和 $y$。则 $x+y=4xy$。将此方程两边同除以 $xy$，得 $\frac{1}{y}+\frac{1}{x}=4$。满足条件的一组数是 $x=\frac{1}{3},\ y=1$。

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