Question

If x=2+√3,find x+1/x

Answer 1

here is your answer...

Answer 2

Hey friend, Harish here.

Here is your answer:

Given that,

x = 2 + √3.

To find,

$x+ \frac{1}{x}$

Solution:

x = 2 + √3. (Given)

$\frac{1}{x} = \frac{1}{2+ \sqrt{3} } = \frac{1}{2+ \sqrt{3} } \times \frac{2- \sqrt{3} }{2- \sqrt{3}} = \frac{2- \sqrt{3} }{4-3} = 2- \sqrt{3}$

 (Here we have rationalized the denominator  of  1 / x.)

Then,

⇒  $x+ \frac{1}{x} = 2+ \sqrt{3} + 2 - \sqrt{3} = 2 + 2 = 4$

$\bold{ Therefore\ the \ answer\ is\ 4}$
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Hope  my answer is helpful to you.