Question

If ( x + 1/x ) = 13 and x > 0, find the value of ( x³ + 1/x³). ​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 13.

As we know that,

Formula of :

⇒ (x + y)³ = x³ + 3x²y + 3xy² + y³.

Using this formula in the equation, we get.

Cubing on both sides of the equation, we get.

⇒ (x + 1/x)³ = (13)³.

⇒ (x)³ + 3(x)²(1/x) + 3(x)(1/x)² + (1/x)³ = (13)³.

⇒ x³ + 3x + 3/x + 1/x³ = 2197.

⇒ x³ + 3(x + 1/x) + 1/x³ = 2197.

Put the values of (x + 1/x) = 13 in the equation, we get.

⇒ x³ + 3(13) + 1/x³ = 2197.

⇒ x³ + 1/x³ + 39 = 2197.

⇒ x³ + 1/x³ = 2197 - 39.

⇒ x³ + 1/x³ = 2158.