If p^2 = q^2, which of the following must be true?  Answers.
A) p =q	B) p = −q	C) p = |k|	D) |p| = |q|	E) p = −|q|
Since p^2=q^2 we have 0=p^2 – q^2 =(p-q)*(p+q). So p=q or p=-q.   So only (A) 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 (E) tells us that k should be less than or equal to 0.   So neither (C) nor (E) cannot be the answer.   The answer is, therefore, (|p| = |q|).
<result>D</result>
If p^2 = q^2, which of the following must be true?