Question

If `x - 3/x = 4, "find"  x^3 - 27/x^3`.

Answer 1

Here, let a = x, b = `3/x`

Using the identity,

a³ − b³ = (a − b)³ + 3ab(a − b)

Thus, 

`(x)^3 - (3/x)^3 = (x - 3/x)^3 + 3xx x  xx3/x(x - 3/x)`

`x^3 - 27/x^3 = (4)^3 + 3xx3xx4`

= 64 + 36

∴ `x^3 - 27/x^3 = 100`