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

As a, b, c are in A.P. given
∴ b = a+c/2
For three numbers, Arithmetic mean ≥ Geometric mean
⇒ a+b+c/3 ≥ (abc)^(1/3)
⇒ Since a, b, c are in A.P., we have a+b+c/3 = b
⇒ 2b+b/3 ≥ (abc)^(1/3)
⇒ b ≥ (abc)^(1/3)
∴ b ≥ 2 since abc = 8