Question

A number is 3 more than its reciprocal what is the difference between their respective cubes?

Answer 1

Answer:

difference between their respective cubes = 36

Step-by-step explanation:

Let say Number = X

Reciprocal = 1/X

to be find :

X³ - (1/X)³  = ?

number is 3 more than its reciprocal

=> X = 3  + 1/X

=> X - 1/X  = 3

Cubing both sides

(X - 1/X)³ = 3³

=> X³  - 1/X³  - 3X(1/X)(X - 1/X)  = 27

=> X³  - 1/X³ - 3(3) = 27

=>  X³  - 1/X³ = 36

difference between their respective cubes = 36