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Question
If x = `5 + 2sqrt6`, then what is the value of `(sqrt"x" + 1/sqrt"x")`?
Options
`2sqrt3`
`3sqrt2`
`2sqrt6`
`6sqrt2`
MCQ
Solution
`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`
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Simplification (Entrance Exam)
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