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:

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Question: Answered & Verified by Expert

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:

MathematicsSequences and SeriesJEE MainJEE Main 2017 (09 Apr Online)

Options:

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

Solution:

1276 Upvotes Verified Answer

The correct answer is:

2

As $a + c = 2 b$ ,

Using $A . M \geq G . M$

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

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

$b \geq 2$

$∴ b_{m i n} = 2$

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