Question

If x= 2+root 3 find x+ 1/x​

Answer 1

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