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March 30th, 2014, 11:46 AM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Inequality challenge
Given some real numbers with prove that 
March 31st, 2014, 08:41 AM  #2 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 
Hint: Consider the polynomial 
March 31st, 2014, 10:03 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
It's easy to show that (4/3)x³ + 1/3 ≥ x for x ≥ 1. Applying that to each numbered x variable and adding gives the desired inequality. 
March 31st, 2014, 10:38 AM  #4 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 
Well done!


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