Question

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

Answer 1

Here, let a = 2x, b = `1/x`

Using the identity,

a³ − b³ = (a − b)³ + 3ab(a − b)

Thus,

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

`8x^3 - 1/x^3 = (1)^3 + 3 xx 2 xx 1`

= 1 + 6

∴ `8x^3 - 1/x^3 = 7`