Question

if a= 2+√3, find the value of a+1/a​

Answer 1

Answer:

$a + \frac{1}{a}= 4$

Step-by-step explanation:

$a = 2 + \sqrt{3} \\ a + \frac{1}{a} \\ = 2 + \sqrt{3} + \frac{1}{2 + \sqrt{3} } \\ = \frac{ {(2 + \sqrt{3} )}^{2} + 1}{2 + \sqrt{3} } \\ = \frac{4 + 3 + 4 \sqrt{3} + 1}{2 + \sqrt{3} } \\ = \frac{8 + 4 \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{4(2 + \sqrt{3} )}{(2 + \sqrt{3}) } \\ = 4$