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If x=sqrt(5)+\ 2, then x-1/x equals (a)...

If `x=sqrt(5)+\ 2,` then `x-1/x` equals
(a)`2sqrt(5)`
(b) 4
(c) 2
(d) `sqrt(5)`

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Solution:
Using identity
`(a+b) xx (a-b) = a^2 - b^2`
`x - 1/x = (1/sqrt(5) + 2 xx sqrt(5) )- (2/sqrt(5) - 2)`
`=sqrt(5) - 2/5-4`
`x - 1/x = sqrt(5) - 2`
`x-1/x =sqrt(5) + 2 - (sqrt(5) -2)`
`=sqrt(5) + 2 -sqrt(5) + 2`
By cancelling, we get
`=4`
Correct option is option `b = 4`
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