Question

If the mean of x and (1/x) is m then mean of x3 and (1/x3) is___

(a) [(8m3 – 6m)/2]

(b) [(8m3 – 3m)/2]

(c) [(3m2 – 8m)/2]

(d) [(3m2 – 8m)/2]

Answer 1

The correct option (a) [(8m3 – 6m)/2]

Explanation:

[{x + (1/x)}/2] = m ⇒ x + (1/x) = 2m

also x3 + (1/x3) = [x + (1/x)]3 – 3[x + (1/x)]

∴ mean of x3 & (1/x3) is given by

(1/2)[x3 + (1/x3)] = (1/2)[{x + (1/x)}3 – 3{x + (1/x)}]

= (1/2)[(2m)3 – 6m]

= (1/2)(8m3 – 6m).