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 March 11th, 2014, 12:01 AM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18 When is it true? If m and n are integers, under what circumstances will m^2 - n^2 be positive? My answer is when |m|>|n|, statement m^2 - n^2 > 0 Is this the correct answer? Is there a better way to see the problem? thanks
March 11th, 2014, 06:36 AM   #2
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Re: When is it true?

Quote:
 Originally Posted by shunya My answer is when |m|>|n|, statement m^2 - n^2 > 0 Is this the correct answer?
Yes, it is correct. It is equivalent to $m\,>\,n\ \text{or}\ m\,<\,-n$.

March 11th, 2014, 06:44 AM   #3
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Re: When is it true?

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 Originally Posted by Nehushtan It is equivalent to $m\,>\,n\ \text{or}\ m\,<\,-n$.
No, (m, n) = (-4, -6) implies m > n or m < -n but m^2 - n^2 < 0.

 March 11th, 2014, 08:30 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,214 Thanks: 2410 Math Focus: Mainly analysis and algebra Re: When is it true? But the OPs answer of |m| > |n| is correct nonetheless.
 March 12th, 2014, 04:36 AM #5 Member   Joined: Mar 2013 Posts: 90 Thanks: 0 Re: When is it true? Sorry, my mistake. $|m|\,>\,|n|$ is equivalent to $m\,>\,\max\{n,\,-n\}\ \text{or}\ m\,<\,\min\{n,\,-n\}$.

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