Question

If x – (1/x) = 3, Evaluate x³ – (1/x³)

Answer 1

x³ – (1/x³)  = 36

Explanation:

Given x - 1/x = 3

Find x³ – (1/x³)

x - 1/x = 3

Squaring on both sides, we get

(x - 1/x)^2 = 3^2

x2 + 1/x2 -2 = 9

x2 + 1/x2 +1 = 12

Applying formula (a – b) (a2 + ab + b2 ), Let's expand

x³ – (1/x³) = (x – 1/x) (x2 + 1/x2 +1)

= 3 * 12

= 36