Question

Given `x - 3/x = 5, "find the value of"  x^3 - 27/x^3.`

Answer 1

Here, `x - 3/x = 5,`

Using the identity,

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

Here, a = 3, so a³ = 27

`(x - 3/x)^3 = x^3 - 27/x^3 - 3(3) (x - 3/x)`

`(5)^3 = x^3 - 27/x^3 - 3(3) (5)`

`125 = x^3 - 27/x^3 - 45`

`125 + 45 = x^3 - 27/x^3`

∴ `x^3 - 27/x^3 = 170`