Question

If three positive real numbers abc are in AP such that abc=4 then the minimum value of b is

Answer 1

Arithmetic mean of 3 nos. Is given by (a+b+c)/3

And geometric mean of 3 nos. Is given by ³√(abc) I.e. cube Root of a*b*c.

According to property A.M >= G.M…(equality holds when all a=b=c)

Applying this property.. we get

(a+b+c)/3 >= ³√(abc)

(a+b+c)/3 >= ³√4

(a+b+c) >= 3× ³√4

But as a,b,c are in A.P.

A+c =2b…..(property of arithmetic mean)

2b+b >= 3 ³√4

3b >= 3 ³√4

B >= ³√4

Which denotes that minimum value of b is ³√4