Question

If `(x^2 + 1)/x = 7, "find" x^3 + 1/x^3`.

Answer 1

`(x^2 + 1)/x = 7`

∴ `x + 1/x = 7`

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 = (7)^3 - 3(7)`

= 343 − 21

∴ `x^3 + 1/x^3 = 322`