Q42 / 90 · JEE Main 2017 (09 Apr Online) · Mathematics

If three positive numbers $a$ , $b$ and $c$ are in A.P. such that $a b c = 8$ , then the minimum possible value of $b$ is:

A
$4^{\frac{2}{3}}$
Correct answer
B
$2$
C
$4^{\frac{1}{3}}$
D
$4$

Solution

As $a + c = 2 b$ ,

Using $A . M \geq G . M$

$\Rightarrow \frac{a + b + c}{3} \geq {(a b c)}^{\frac{1}{3}}$

$\Rightarrow \frac{3 b}{3} \geq {(8)}^{\frac{1}{3}}$

$b \geq 2$

$∴ b_{m i n} = 2$

Hence, the correct answer is option: 'B'.

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