Question

If x-1/x=5 ,then x^3-1/x^3=

Answer 1

The answer is given below :

By identity, we know that

a³ - b³ = (a - b)³ + 3ab(a - b)

Given that,

x - 1/x = 5

Now,

x³ - 1/x³ = (x - 1/x)³ + (3 × x × 1/x)(x - 1/x)

= 5³ + (3 × 5)

= 125 + 15

= 140 [Ans.]

Thank you for your question.

Answer 2

Given
x - 1/x = 5

We know that
x³ - 1/x³ =  (x - 1/x)³ + 3(x - 1/x)
             = (5)³ + 3(5)
             = 125 + 15
             = 140

x³ - 1/x³ = 140.

Hope this helps you.