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Problem 660

AMC 10/12, early questions

Algebra Difficulty 3.8 Find the answer China Mathematical Competition · China

Given $A = \{2, 0, 1, 3\}$ , let $B = \{x \mid -x \in A, 2 - x^2 \notin A\}$ . Then the sum of elements in $B$ is ______.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

It is easy to find that $B \subseteq \{-2, 0, -1, -3\}$ . We have $2 - x^2 \notin A$ when $x = -2, -3$ , and $2 - x^2 \in A$ when $x = 0, -1$ . Therefore, $B = \{-2, -3\}$ , the sum of whose elements is $-5$ .
The answer is $-5$ .

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