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October 24th, 2016, 10:13 AM  #1 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Verify rule for absolute value
Hi guys, could someone help on how to tackle these two problems I am not quite how to tackle these. I think the first one is a triangle inequality but not too sure? I really donâ€™t know about the second. Do I use the equation given and start from there or do I derive it some how from an absolute value.I can see if i plug number in it works but that it really. Questions are below: Q1. Verify the rule that for two real numbers x and y then $\displaystyle x+y < xy$ (suppose to be less than equal too) Q2. Given that for two real numbers x and y, $\displaystyle x+y<x+y$, deduced that $\displaystyle xy<xy$ (once again suppose to be less than equal to.) 
October 24th, 2016, 01:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,235 Thanks: 497 
They are both wrong. Counterexamples: for Q1, let x=y, while for Q2 let x=y.


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