Minimum Value

Algebra Level 3

If three positive real numbers a,b,c are in A.P, then find the minimum value of b if $abc=8$

8 2 1 4

1 solution

Sujoy Roy
Aug 2, 2015

$\frac{a+b+c}{3}\ge (abc)^{1/3}$ or, $\frac{b+2b}{3}\ge (8)^{1/3}$ or, $b\ge 2$ .

Thus, minimum value of $b$ is $\boxed{2}$ .