If x^2 = y^2, which of the following must be true?  Pick one.
A) x = y  B) x = −y  C) |x| = |y|  D) x = −|y|  E) x = |y|
Since x^2=y^2 we have 0=x^2 – y^2 =(x-y)*(x+y). So x=y or x=-y.   So only (A) and only (B) cannot be an answer.   The choice (E) 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 (E) nor (D) cannot be the answer.   The answer is, therefore, (|x| = |y|).
<result>C</result>
If x^2 = y^2, which of the following must be true?