AMC10 2007 A

AMC10 2007 A · Q2

AMC10 2007 A · Q2. It mainly tests Algebra misc.

Define $a@b = ab - b^2$ and $a\#b = a + b - ab^2$. What is $6@2 \div 6\#2$?

定义 $a@b = ab - b^2$ 和 $a\#b = a + b - ab^2$。求 $6@2 \div 6\#2$ 的值？

(A) $-\frac{1}{2}$ $-\frac{1}{2}$

(B) $-\frac{1}{4}$ $-\frac{1}{4}$

(D) $\frac{1}{4}$ $\frac{1}{4}$

(E) $\frac{1}{2}$ $\frac{1}{2}$

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The value of $6@2$ is $6\cdot2-2^2=12-4=8$, and the value of $6\#2$ is $6+2-6\cdot2^2=8-24=-16$. Thus $$\frac{6@2}{6\#2}=\frac{8}{-16}=-\frac{1}{2}.$$

答案（A）：$6@2$ 的值为 $6\cdot2-2^2=12-4=8$，而 $6\#2$ 的值为 $6+2-6\cdot2^2=8-24=-16$。因此 $$\frac{6@2}{6\#2}=\frac{8}{-16}=-\frac{1}{2}.$$

Topics

AL.020 Algebra misc