2021 AMC 10A Spring 第 1 题

Question

求下式的值：

(2^2-2)-(3^2-3)+(4^2-4)\text{？}

What is the value of

(2^2-2)-(3^2-3)+(4^2-4)?

1

2

5

8

12

先分别计算括号里的每一项，再处理前面的正负号。

Evaluate each parenthesized expression before combining the signs

注意每一项都有

n^2-n

的形式。

Notice that each term has the form

n^2-n

\begin{aligned} (2^2 - 2) - &(3^2 - 3) + (4^2 - 4) \\ &= 2 - 6 + 12 \\ &= 8 \end{aligned}\text{。}

所以正确答案是 D。

\begin{aligned} (2^2 - 2) - &(3^2 - 3) + (4^2 - 4) \\ &= 2 - 6 + 12 \\ &= 8. \end{aligned}

Thus, D is the correct answer.

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