Question

If a=2+√3 find a+1/a

Answer 1

Step-by-step explanation:

$\frac{a + 1}{a} \\ \frac{2 + \sqrt{3} + 1}{2 + \sqrt{3} } \\ \frac{3 + \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{(3 + \sqrt{3} )(2 - \sqrt{3} )}{(2 + \sqrt{3}) (2 - \sqrt{3} )} \\ \frac{6 - 3 \sqrt{3} + 2 \sqrt{3} - 3}{ {2}^{2} - ( { \sqrt{3} )}^{2} } \\ \frac{3 - \sqrt{3} }{4 - 3} \\ \frac{3 - \sqrt{3} }{1} \\ = 3 - \sqrt{3} \\ = \sqrt{3} ( \sqrt{3} - 1)$