If a, b, c are three distinct positive real numbers, then the least value of
`((1+a+a^(2))(1+b+b^(2))(1+c+c^(2)))/(abc)`, is

Options

A. 3
B. 9
C. 27
D. none of these

Answer

C

Explanation

For any `xgt0`, we have
`(1+x+x^(2))/(x)=(x+(1)/(x))+1ge2+1-3`
`:." "((1+a+a^(2))(1+b+b^(2))(1+c+c^(2)))/(abc)`
`=((1+a+a^(2))/(a))((1+b+b^(2))/(b))((1+c+c^(2))/(c))ge3xx3xx3=27`
Hence, the least value of the given expression is 27 which it attains when `a=b=c=1`.