Question

If `x - 1/x = 3`, then the value of `x^3 - 1/x^3` is ______.

पर्याय

• 27

• 36

• 45

• 18

Answer 1

If `x - 1/x = 3`, then the value of `x^3 - 1/x^3` is 36.

Explanation:

Let’s solve step-by-step:

1. Given `x - 1/x = 3`, we want to find `x^3 - 1/x^3`.

2. We use the identity:

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

3. Substitute `x - 1/x = 3`:

`3^3 = x^3 - 1/x^3 - 3 xx 3`

`27 = x^3 - 1/x^3 - 9`

4. Rearrange to find `x^(3) - 1/x^3`:

`x^3 - 1/x^3 = 27 + 9`

`x^3 - 1/x^3 = 36`

Hence, the value of `x^3 - 1/x^3` is 36.