Question

If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.

If `(x^2 + 1)/x = 3 1/3  "find"  x - 1/x`.

Answer 1

Given `(x^2 + 1)/x = 3 1/3`

`(x^2 + 1)/x = 10/3`

`x + 1/x = 10/3`

Squaring on both sides, we get

= `(x + 1/x)^2 = (10/3)^2`

= `x^2 + 1/x^2 + 2 = 100/9`

= `x^2 + 1/x^2 = 100/9 - 2`

= `x^2 + 1/x^2 = (100 - 18)/9`

∴ `x^2 + 1/x^2 = 82/9`

Also,

`x - 1/x = sqrt((x + 1/x)^2 - 4)` 

= `sqrt(100/9 - 4)`

= `sqrt(64/9)`

∴ `x - 1/x = 8/3`