AMC10 2002 A

AMC10 2002 A · Q2

AMC10 2002 A · Q2. It mainly tests Fractions.

For the nonzero numbers $a$, $b$, and $c$, define $(a, b, c) = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$. Find $(2, 12, 9)$.

对于非零数 $a$、$b$ 和 $c$，定义 $(a, b, c) = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$。求 $(2, 12, 9)$ 的值。

(A) 4 4

(B) 5 5

(D) 7 7

(E) 8 8

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) We have \[(2,12,9)=\frac{2}{12}+\frac{12}{9}+\frac{9}{2}=\frac{1}{6}+\frac{4}{3}+\frac{9}{2}=\frac{1+8+27}{6}=\frac{36}{6}=6.\]

（C）我们有 \[(2,12,9)=\frac{2}{12}+\frac{12}{9}+\frac{9}{2}=\frac{1}{6}+\frac{4}{3}+\frac{9}{2}=\frac{1+8+27}{6}=\frac{36}{6}=6.\]

Topics