यदि `x=5+2sqrt(6)`, है तो `(sqrt(x)+1/(sqrt(x)))` का मान क्या होगा?

Options

A. `2sqrt(2)`
B. `3sqrt(2)`
C. `2sqrt(3)`
D. `sqrt(3)`

Answer

C

Explanation

`x=5+2sqrt(6)`
`x=3+2+2sqrt(3)xxsqrt(2)`
`x=(sqrt(3))^(2)+(sqrt(2))^(2)+2sqrt(3)xxsqrt(2)`
`x=(sqrt(3)+sqrt(2))^(2)`
`sqrt(x)=sqrt(3)+sqrt(2)`
Similarly
`implies1/(sqrt(x))=sqrt(3)-sqrt(2)`
`sqrt(x)+1/(sqrt(x))=sqrt(3)+sqrt(2)+sqrt(3)-sqrt(2)`
`=2sqrt(3)`