Question

if average of two numbers x and 1/x is 4 what will be the average of x^3 amd 1/x^3

Answer 1

Average of x and 1/x = 4

So,

(x+1/x)/2 = 4

Or, x+1/x = 8

Now, average of x^3 and 1/x^3 = (x^3+1/x^3)/2

= {(x+1/x)^3 - 3(x+1/x)}/2 [ by formula]

= {(8^3) - (3×8)}/2 [ since x+1/x = 8 ]

= (512 - 24)/2

= 488/2

= 244 (ANS)