Question

x=7-4√3;then √x+1/√x=?

Answer 1

x = 7 - 4√3

1/x = 1/(7 - 4√3) * (7 + 4√3)/(7 + 4√3)

1/x = (7 + 4√3)/(49 - 48)

1/x = (7 + 4√3)

now,
(√x + 1/√x)² = x + 1/x + 2*√x *1/√x

(√x + 1/√x)² = (7 - 4√3) + (7 - 4√3) + 2

(√x + 1/√x)² = 14 + 2

(√x + 1/√x)² = 16

(√x + 1/√x) = 4.