Question

If x=2+root3
Find x+1/x​

Answer 1

Here's the required answer to your question

Answer 2

Given,

$x = 2 + \sqrt{3}$

To find - x + 1/x

$= (2 + \sqrt{3} ) + ( \frac{1}{2 + \sqrt{3} } ) \\ rationalising \: the \: denominator \\ = 2 + \sqrt{3} + ( \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } ) \\ \\ = 2 + \sqrt{3} + ( \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } ) \\ \\ = 2 + \sqrt{3} + ( \frac{2 - \sqrt{3} }{4 - 3} ) \\ \\ = 2 + \sqrt{ 3} + ( \frac{2 - \sqrt{3} }{1} ) \\ \\ = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ = 4 + 0 \\ \\ = 4$