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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2010-01-28 09:28:29

Shiiro
Member
Registered: 2009-11-30
Posts: 27

Inequality

Hi !

,
. Prove That :

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#2 2010-01-29 01:33:45

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Inequality

Fully expanding:

Factoring nicely:

AM-GM

AM-HM

Therefore, putting it all together,

Last edited by Identity (2010-01-29 01:40:51)

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#3 2010-01-30 04:22:05

Emo
Guest

Re: Inequality

Hi !!




by  AM-GM :


 
 

And We Have :


 
   

by add

and
We Have The result sought ! wink

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