Question

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

Answer 1

Here, `x + 3/x = 4,`

Using the identity,

a³ + b³ = (a + b)³ − 3ab(a + b)

Let’s take a = x and b = `3/x`

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

= (4)³ − 3(3)(4)

= 64 − 3(12)

= 64 − 36

∴ `x^3 + 27/x^3` = 28