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Question
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
Solution
`sqrt(x) + (1)/(sqrt(x)`
Squaring Both sides we get
`(sqrt(x) + (1)/sqrt(x))^2 = x + (1)/x + 2` ----(1)
We will first find out `x + (1)/x`
`x + (1)/x = (7 + 4sqrt(3)) + (1)/((7 + 4sqrt(3))`
= `((7 + 4sqrt(3)^2 + 1))/((7 + 4sqrt(3))`
= `(49 + 48 + 56sqrt(3) + 1)/((7 + 4sqrt(3))`
= `(98 + 56sqrt(3))/((7 + 4sqrt(3))`
= `(14(7 + 4sqrt(3)))/((7 + 4sqrt(3))`
= 14
substitutingin (1)
`(sqrt(x) + (1)/sqrt(x))^2 = x + (1)/x + 2`
= 14 + 2
= 16
∴ `sqrt(x) + (1)/sqrt(x)` = 4
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