每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If (x + y)^2 = (x^2) + (y^2), which of the following statements must also be true?

1. x = 0
2.(x-y)^2 = (x^2) + (y^2)
3. xy = 0

(A) None
(B) 1 only
(C) 2 only
(D) 3 only
(E) 2 and 3

答案和解析

答案：E

解析：

The quantity (x + y)^2 can be expressed as (x^2) + (2xy) + (y^2). If (x + y)^2 = (x^2) + (y^2), then 2xy = 0 and xy = 0. Since xy = 0, either x = 0 or y = 0 or both. Therefore, statement 3 must be true, but statement 1, x = 0, is not always true. For statement2, you can write (x-y)^2 = (x^2)-(2xy) + y^2, and since xy = 0, it follows that (x-y)^2 = (x^2) + (y^2). Therefore, both statements 2 and 3 must be true.