Question

If x=2+root 3, then:
x+1/x

Answer 1

this is the right answer

Answer 2

$given \: x = 2 + \sqrt{3} \\ \\ put \: x = 2 + \sqrt{3} \: in \: \frac{x + 1}{x} \\ \\ \frac{2 + \sqrt{3 } + 1 }{2 + \sqrt{3} } \\ \\ \frac{3 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ rationalise \: the \: denominator$

$\frac{3 + \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{(3 + \sqrt{3})(2 - \sqrt{3} ) }{ {2}^{2} - ( \sqrt{3} ) {}^{2} } \\ \\ (herefore \: (a + b)(a - b) = {a}^{2} - {b}^{2} ) \\ \\ \frac{(3 + \sqrt{3} )(2 - \sqrt{3}) }{4 - 3} \\ \\ (3 + \sqrt{3} )(2 - \sqrt{3} ) \\ \\ 6 - 3 \sqrt{3} + 2 \sqrt{3} - ( { \sqrt{3} )}^{2} \\ \\ 6 - \sqrt{3} - 3 \\ \\ 3 - \sqrt{3}$