1.

If alpha+beta, gamma epsilon R^(+) such that alpha gamma =1/(beta) then maximum value of alpha^(beta+gamma), .beta^(beta+gamma).gamma^(alpha+beta) is_____

Answer»


SOLUTION :`beta=1/(alpha GAMMA)`
Assume `alpha GE beta ge gamma` (SAY)
`impliesalpha ge 1` and `gamma LE1`
`:.(alpha^(beta+gamma).gamma^(alpha+beta))/((alpha gamma)^(alpha+gamma))=(gamma^(beta-gamma))/(alpha^(alpha-beta)) le 1`


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