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).