If x + 1/x = 3, then what is the value of x³ + 1/x³?

If x + 1/x = 3, then what is the value of x³ + 1/x³?

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

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

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18