Question

If `(x^2 - 1)/x = 8, "find"  x^3 - 1/x^3`.

Answer 1

Here, `(x^2-1)/x=8`

∴ `x - 1/x = 8`

Let’s take a = x, b = `1/x`,

Using the identity:

a³ − b³ = (a − b)³ + 3ab(a − b)

Thus,

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

`x^3 - 1/x^3 = (8)^3 + 3(8)`

= 512 + 24

∴ `x^3 - 1/x^3 = 536`