Question

If x² − 9x + 1 = 0, find the value of `x+1/x and x^3 + 1/x^3.`

Answer 1

Here, x² − 9x + 1 = 0,

Dividing both sides of the equation by x,

`x^2/x - (9x)/x + 1/x = 0/x`

`x - 9 + 1/x = 0`

`∴ x + 1/x = 9`

Using the identity,

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

`(9)^3 = x^3 + 1/x^3 + 3(9)`

`729 = x^3 + 1/x^3 + 27`

`x^3 + 1/x^3 = 729 - 27`

∴ `x^3 + 1/x^3 = 702`