Question

If x = `5 + 2sqrt6`, then what is the value of  `(sqrt"x" + 1/sqrt"x")`?

विकल्प

• `2sqrt3`

• `3sqrt2`

• `2sqrt6`

• `6sqrt2`

Answer 1

`2sqrt3`

Explanation:

x = `5 + 2sqrt6`

`sqrt"x" = sqrt3 + sqrt2`

⇒ `sqrt"x" + 1/sqrt"x" = sqrt3 + sqrt2 + 1/(sqrt3 + sqrt2)`

⇒ `sqrt"x" + 1/sqrt"x" = sqrt3 + sqrt2 + sqrt3 - sqrt2`

= `2sqrt3`