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#1 2010-02-04 06:03:22

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

Inequality ...

Hii !

a, b and c the réels posifives numbers , prove That :


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#2 2010-02-04 06:54:20

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Inequality ...

We have

which is always non-negative for all

, i.e.

Same for all

and
; adding up gives the required inequality.

NB: This particular method of tackling inequalities is especially useful when there are no restrictions on how the variables vary with respect to each other and we can neatly separate out the variables into part sums.

Last edited by JaneFairfax (2010-02-04 08:59:33)

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