If a^2 = b^2, which of the following must be true? Choose the correct choice from the following answers:
A) |a| = |b|
B) a = −b
C) a = |b|
D) a = −|b|
E) a = b
Since a^2=b^2 we have 0=a^2 – b^2 =(a-b)*(a+b). So a=b or a=-b.   So only (E) and only (B) cannot be an answer.   The choice (C) tells us that k should be greater than or equal to 0.   Similarly the choice (D) tells us that k should be less than or equal to 0.   So neither (C) nor (D) cannot be the answer.   The answer is, therefore, (|a| = |b|).
<result>A</result>
If a^2 = b^2, which of the following must be true?