If `l ,m ,n` are the three positive roots of the equation `x^3-a x^2+b x-48=0,` then the minimum value of `(1//l)+(2//m)+(3//n)` equals `1` `2` `3//2` `5//2`

Options

A. 1
B. 2
C. `3//2`
D. `5//2`

Answer

C

Explanation

Consider 1/l, 2/m, 3/n and use A.M `ge` G.M. Then
`:. (1)/(3) ((1)/(l) + (2)/(m) + (2)/(n)) ge ((6)/(48))^(1//3) = (1)/(2)`
`:. ((1)/(l) + (2)/(m) + (3)/(n))_("min") = (3)/(2)`