Question

Sum of a number and its reciprocal is 4 then value of sum of cube of the number and reciprocal of the cube is

Answer 1

Let the number be x

By given condition,
x + 1/x = 4

x³+(1/x)³ = ?

a³ + b³ = (a + b) (a² - ab + b² )

x³+(1/x)³  = (x + 1/x)(x² - x(1/x) + (1/x)²)

                = 4(x² + (1/x)² - 1)

(a + b)² = a² + 2ab + b²

 a²  + b² = (a + b)² -  2ab 

x² + (1/x)² = 4² - 2 x(1/x) = 16 - 2 = 14

Thus,

x³+(1/x)³  = 4(14 - 1) = 52

Answer 2

Answer:

just a smart trick :

If x+1/x=a,

then x^3+1/x^3 = a ^3-3a

Here, a=4

x^3 + 1/x^3= 4^3-3×4

64-12 = 52 //....