If three positive numbers a, b and c are in A.P.

Question

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

Accepted Answer

a, b and c are in AP.

$$ \therefore $$ a + c = 2b

As, abc = 8

$$ \Rightarrow $$ac$$\left( {{{a + c} \over 2}} \right)$$= 8

$$ \Rightarrow $$ ac(a + c) = 16 = 4 $$ \times $$ 4

$$ \therefore $$ ac = 4 and a + c = 4

Then,

b = $$\left( {{{a + c} \over 2}} \right)$$ = $${4 \over 2}$$ = 2

Solutions · 1