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

Question

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

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_____

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 1
`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`

4 views Answered 2023-02-05 15:29