If `x = 3 + 2 sqrt2`, then find the value of `x + (1)/(x)`

Explanation

Given that `x = 3 + 2 sqrt2`
`:. (1)/(x) = (1)/(3 + 2 sqrt2) = (1)/(3+ 2 sqrt2) xx (3-2 sqrt2)/(3 - 2 sqrt2)`
`= (3-2sqrt2)/((3)^(2) - (2 sqrt2)^(2)) = (3 - 2 sqrt2)/(9 -8)`
`= (3 - 2 sqrt2)/(1) = 3 -2 sqrt2`
`:. x + (1)/(x) =3 + 2sqrt2 + 3 -2 sqrt2 = 6`
`:.` The required summation = 6