theorem on weighted means

'theorem on weighted means' is in iit jee syllabus ? If yes , where can i get some good problems to master that topic.....??

2 Answers

Find the maximum value of a²b³c⁴, when a,b,c all are positive real numbers and a+b+c = 6

consider the numbers : a/2 ,a/2,b/3(3 times) and c/4(4 times)

from the inequality amâ‰¥gm,
(a+b+c)/9 â‰¥ {a²b³c⁴/(2²3³4⁴)}^1/9

from this i got the maximum as 2¹⁸3⁹4¹³6⁹ ......correct?

Can you explain the theorem on weighted means?(actually i don't know it )...then i'll try to solve this using that meathod ...

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