Question

If a,b,c are positive, then the minimum value of the expression $\frac{(a^2+a+1)(b^2+b+1)(c^2+c+1)}{abc}$ is:

• A. 3
• B. 9
• C. 27
• D. 1

Answer 1

The correct option is C 27

The expression will have minimum value when a = b = c because then abc will have a maximum value.
Therefore, the required minimum value
$=\frac{1+1+1}{1}\times \frac{1+1+1}{1}\times \frac{1+1+1}{1}=27$