If |x| - |y| = |x+y| and xy not equal zero , which of the following must be true ?
Choose the correct choice from the following answers:
A) x-y> 0
B) x-y< 0
C) x+y> 0
D) xy>0
E) xy<0
|x| - |y| = |x+y|   =&gt; (|x| - |y|)^2 = |x+y|^2 = (x+y)^2   =&gt; x^2 - 2|x||y| + y^2 = x^2 + 2xy + y^2   =&gt; |xy| = -xy   because xy != 0 so xy &lt;0   Ans: xy&lt;0
<result>E</result>
If |x| - |y| = |x+y| and xy not equal zero , which of the following must be true ?