Question

if x=7+4√3, find the value of√x+1/√x

Answer 1

$\textbf{\underline{Answer :}}$

Given that,

x = 7 + 4√3

= 4 + 4√3 + 3

= 2² + (2 × 2 × √3) + (√3)²

= (2 + √3)²

⇒ √x = 2 + √3

Now, 1/√x = 1/(2 + √3)

= (2 - √3)/{(2 + √3)(2 - √3)}

= (2 - √3)/(4 - 3)

= (2 - √3)/1

= 2 - √3

[We did rationalize the denominator of the term only.]

Now, √x + 1/√x

= 2 + √3 + 2 - √3

= 4

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