Question

If x=2+√3, find the value of x+1/x

Answer 1

HEY !!!!

HERE IS UR ANSWER-------

Given,

x = 2 + √3

1/x = 1 / 2 + √3

On rationalizing the denominator,

= (1 / 2 + √3) × (2 - √3 / 2 - √3)

= 2 - √3 / (2)^2 - (√3)^2

= 2 - √3 / 4 - 3

= 2 - √3

Therefore ,

x + 1/x

= 2 + √3 + 2 - √3

= 2 + 2

= 4.

Answer 2

hey brother!

Here is your Answer!

X = 2+√3

then

==> 1/X = 1/2+√3

now multiply 2-√3 both side

==>
$\frac{2 - \sqrt{3} }{ {2}^{2} - \sqrt{3 {}^{2} } } \\ \\ = \frac{2 - \sqrt{3} }{4 - 3 } \\ \\ = 2 - \sqrt{3} \\ \\ so \: x + \frac{1}{x} = 2 + \sqrt{3 } + 2 - \sqrt{3} \\ \\ x + \frac{1}{x} = 4 \: ans$