If a, b, c are positive real numbers, then the minimum value of `a^(logb-logc)+b^(logc-loga)+c^(loga-logb)`isA. 3B. 1C. 9D. 16

If a, b, c are positive real numbers, then the minimum value of `a^(lo

1.	If a, b, c are positive real numbers, then the minimum value of `a^(logb-logc)+b^(logc-loga)+c^(loga-logb)`isA. 3B. 1C. 9D. 16
Answer» Correct Answer - A Using `A.M.geG.M.,` we have `(a^(logb-logc)+b^(logc-loga)+c^(loga-logb))/(3)` `ge{a^(logb-logc)xxb^(logc-loga)xxc^(loga-logb)}^(1//3)` Let `a^(logb-logc)xxb^(logc-loga)xxc^(loga-logb)=lambda`.Then, `loglambda=(logb-logc)loga+(logc-loga)logb+(loga-logb)logc` `implies" "loglambda=0implieslambda=1` `a^(logb-logc)+b^(logc-loga)+c^(loga-logb)ge3` Hence, the minimum value of `a^(logb-logc)+b^(lobc-loga)+c^(loga-logb)`is 3.

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