SOLUTION: Prove that if |x + y| = |x| + |y| then xy > 0

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Question 1195702: Prove that if |x + y| = |x| + |y| then xy > 0
Answer by ikleyn(52800) About Me  (Show Source):
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Prove that if |x + y| = |x| + |y| then xy > 0
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This statement is  INCORRECT,  i.e.  WRONG.


The counter-example is  x= 0,  y= 0.


Another counter-example is  x= 0  and  y  is any real number.


Third counter-example is  y= 0  and  x  is any real number.