Question

Guys please solve this question quickly, I don't understand this

Answer 1

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

Taking square root on both sides
√x = +- 2+√3

Now,
√x+1/√x
= x + 1. / √x
= 7+4√3 + 1 /2+√3
= 8+4√3 / 2+√3
then rationalise this

Similarly
= 7+4√3 +1/-2-√3
and rationalise this

Answer 2

First of all, notice that 

7 + 4 sqrt(3) 

= 4 + 2 sqrt(3) + 2 sqrt(3) + 3 

= (2 + sqrt(3))^2 

Now, since 

√x + 1/√x = (x + 1) / sqrt(x), 

Substitute 7 + 4 sqrt(3) for x: 

= (7 + 4 sqrt(3) + 1) / sqrt(7 + 4 sqrt(3)) 

Collect terms: 

= ( 8 + 4 sqrt(3)) / (2 + sqrt(3)) 

Factor the numerator: 

= 4 [ ( 2 + sqrt(3) ) / (2 + sqrt(3)) ] 

= 4 (1) 

= 4