x = 7 + 4√3

Now, √x = √( 7 + 4√3 ) = √ [(√4)^2 + (√3)^2 + 2x√4x√3)]
√x = (√4) + (√3) = 2 + √3

1 / √x = 1 / ( 2 + √3 )
Rationalizing the denominator, we get,
1 / √x = 2 – √3

So, √x + 1 / √x = 2 + √3 + 2 – √3 = 4