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[Post New]17 Mar 2007 18:33:52 IST
    Subject: Re:Progression
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iitkgp_bipin (6480)

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Olaaa!! Perrrfect answer. 1104  bad job dude!! I dont approve of this answer! 1  [1586 rates]
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Split a+b+c in a/2+a/2+b/3+b/3+b/3+c/4+c/4+c/4+c/4

Now using AM>=GM

(a+b+c)/9 >= (a/2xa/2xb/3xb/3xb/3xc/4xc/4xc/4xc/4)1/9 

a2b3c4 <= (18/9)9223344

a2b3c4 <= 426384

Hence maximum value of a2b3c4 is 426384

In such type of problems greatest value can be found by taking ratios of a,b,c powers.

a:b:c: = 2:3:4
a+b+c=18
a=4  b=6  c=8

a2b3c4 = 426384  (maximum value)
Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur

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