Question

If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.

Answer 1

Given: x = `sqrt(7) - 2`

⇒ `1/x = 1/(sqrt(7) - 2)`

= `1/(sqrt(7) - 2) xx (sqrt(7) + 2)/(sqrt(7) + 2)`

= `((sqrt(7) + 2))/((sqrt(7) - 2)(sqrt(7) + 2))`

= `((sqrt(7) + 2))/((sqrt(7))^2 - (2)^2) = ((sqrt(7) + 2))/(7 - 4)`

= `((sqrt(7) + 2))/3`

Now, `(x + 1/x) = sqrt(7) - 2 + ((sqrt(7) + 2))/3`

= `(3sqrt(7) - 6 + sqrt(7) + 2)/3`

= `(4sqrt(7) - 4)/3`

Hence, the value of `(x + 1/x)` is `(4sqrt(7) - 4)/3`.