Question

If `x+1/x = 2, "find"  x^3+1/x^3.`

Answer 1

Here, `x + 1/x = 2`

So, let a = x, b = `1/x`

Using the identity,

a³ + b³ = (a + b)³ − 3ab(a + b)

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

= (2)³ − 3(1) (2)

= 8 − 6

∴ `x^3 + 1/x^3` = 2