If x=7+√3, find the value of √x+1\√x

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Solution

Sol:
Given x = 7 + 4√3

x = 7 + 4√3

1 / x = 1 / ( 7 + 4√3) rationalize denominator (7 - 4√3)

= (7 - 4√3) / 49 - 48 = (7 - 4√3)
√x = √( 7 + 4√3 ) = √ ( √4)2 + (√3)2 + 2x√4x√3 )

√x = √4) + (√3) = 2 + √3 .

⇒ 1 / √x = 1 / ( 2 + √3 ) rationalize denominator (2 - √3) then

⇒ 1 / √x = 2 - √3

Therefore,

√x +1 / √x = 2 + √3 + 2 - √3 = 4

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