If the average of a number and its reciprocal is 2, then the average of its cube and its reciprocal is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 26.
Let the number be x
The average of a number and its reciprocal is 2
⇒ (x + 1/x)/2 = 2
⇒ x + 1/x = 4
Cubing both sides
⇒ (x + 1/x)3 = 43
⇒ x3 + 1/x3 + 3(x + 1/x) = 64
⇒ x3 + 1/x3 + 3 × 4 = 64
⇒ x3 + 1/x3 + 12 = 64
⇒ x3 + 1/x3 = 52
The average = (x3 + 1/x3)/2 = 52/2 = 26
Hence, The average of the cube and its reciprocal is 26