AMC10 2006 B

AMC10 2006 B · Q2

AMC10 2006 B · Q2. It mainly tests Functions basics.

For real numbers $x$ and $y$, define $x \ast y = (x + y)(x - y)$. What is $3 \ast (4 \ast 5)$?

对于实数 $x$ 和 $y$，定义 $x \ast y = (x + y)(x - y)$。什么是 $3 \ast (4 \ast 5)$？

(A) -72 -72

(B) -27 -27

(D) 24 24

(E) 72 72

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Because $4\spadesuit 5=(4+5)(4-5)=-9$, it follows that $3\spadesuit(4\spadesuit 5)=3\spadesuit(-9)=(3+(-9))(3-(-9))=(-6)(12)=-72.$

（A）因为 $4\spadesuit 5=(4+5)(4-5)=-9$，所以 $3\spadesuit(4\spadesuit 5)=3\spadesuit(-9)=(3+(-9))(3-(-9))=(-6)(12)=-72。$

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