My Math Forum Help - inequality

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 October 17th, 2009, 01:39 AM #1 Newbie   Joined: Oct 2009 Posts: 4 Thanks: 0 Help - inequality Hi there! English is not my first language, so I apologize for my writing. I need help solving this inequality: $\frac{1}{a^2+2} + \frac{1}{b^2+2} + \frac{1}{c^2+2} \leq \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{abc}}$ Thanks in advance!
 October 17th, 2009, 03:18 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,484 Thanks: 2041 Are you given that a, b, and c are all positive?
 October 17th, 2009, 03:41 AM #3 Newbie   Joined: Oct 2009 Posts: 4 Thanks: 0 Re: Help - inequality Yes. Sorry, I forgt to mention that condition.
 October 17th, 2009, 06:58 PM #4 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Where did you got the problem, Razzvy?
 October 17th, 2009, 11:28 PM #5 Newbie   Joined: Oct 2009 Posts: 4 Thanks: 0 Re: Help - inequality I got it from my IXth grade exercise book, but I managed to show that it is wrong. If you want, I can post how I did it. Sorry
 October 18th, 2009, 10:40 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,484 Thanks: 2041 The inequality is false if a = 1 and b = c = 25. Perhaps some other condition on a, b, and c was omitted.

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