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Algebra

Hot goIITian

Joined:	24 Apr 2008
Post:	163

2 May 2008 13:22:52 IST

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596

solve it if u can!!!

None

solve it if u can!!!

find minimum of $\Sigma$ (a^2 + 1)/ (b+c) where a,b,c cyclically change and a,b,c>0

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Decoder

Blazing goIITian

Joined: 1 Apr 2007

Posts: 1084

2 May 2008 15:42:17 IST

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i can ?? obviously yaar!! .. so here is the soln.

we know by simple inequality tht...

a^2 + 1 >= 2a...

b^2 + 1 >= 2b..

u get something wic is very common i.e.

2 { a / (b+c) ....} .. term inside itself is 6 ... ( basic derivatuions frm a.m-h.m)

wic is nothing but 12..

Celestine Preetham

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 19:07:31 IST

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SORRY WRONG ANS

animal

Hot goIITian

Joined: 5 May 2008

Posts: 194

5 May 2008 12:33:24 IST

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Is the ans =1.

sandeep ramesh

Blazing goIITian

Joined: 13 Mar 2008

Posts: 1183

5 May 2008 12:43:58 IST

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as decoder said given expr $\ge 2\sum_{cyc} \frac{a}{b+c} \ge 2 * \frac{3}{2} = 3$

See Nesbitt's inequality

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