Question

If X=4+2√3 then find thd value of √x+1/√X

Answer 1

Answer:

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

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