Question

if x=2+√3, find (x+1/x)

Answer 1

$\bf \red{ x = 2 + \sqrt{3}} \\ \\ \\ \bf\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ \\ \bf \frac{1}{x} = \frac{1}{(2 + \sqrt{3} )} \times \frac{(2 - \sqrt{3}) }{(2 - \sqrt{3} )} \\ \\ \bf\frac{1}{x} = \frac{2 - \sqrt{3} }{ {2}^{2} - { (\sqrt{3} )}^{2} } \\ \\ \bf \: \frac{1}{x} = \frac{2 - \sqrt{3} }{1} \\ \\ \bf \red{\frac{1}{x} = 2 - \sqrt{3}} \\ \\ \\ \bf \: x + \frac{1}{x} = (2 + \sqrt{3} ) + (2 - \sqrt{3} ) \\ \\ \large \bf \blue{ x + \frac{1}{x} = 4}$

Answer 2

Answer:

refer to the attachment