Question

If x = 2 + √3, what is the value of x+1/x
?​

Answer 1

Answer:

4

step-by-step explanation:

Given :  $x = 2 + \sqrt{3}$

To Find : find the value of   $\frac{1}{x}$

Solution:

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

Since  , $x = 2 + \sqrt{3}$

to find ,    $\frac{1}{x}$

$x = 2 + \sqrt{3}$

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

∴  $\frac{1}{x} = 2 - \sqrt{3}$

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

$= 2 + \sqrt{3} + 2 - \sqrt{3} = 4$

$hence , x + \frac{1}{x} = 4$