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If three distinct positive numbers $a, b, c$ are in A.P. such that $a b c = 4,$ then value of b is always

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greater than $(2)^{2 / 3}$

less than $(2)^{2 / 3}$

equal to $(2)^{2 / 3}$

equal to $(2)^{3 / 2}$

answer is A.

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Detailed Solution

$3 b = a + b + c \geq 3 (a b c)^{1 / 3}$

$\Rightarrow b \geq 4^{1 / 3} = 2^{2 / 3}$

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