Question

If a=2+√3, then find the value of a+1/a.

Answer 1

Answer:4

Step-by-step explanation:a+1/a

(a^2)+1/a

(2+√3)^2+1/2+√3

4+3+4√3+1/2+√3

8+4√3/2+√3

4(2+√3)/2+√3

4 ans

Hope it will help you

Answer 2

Answer:

The value of a+1/a =

Step-by-step explanation:

Given

$a = 2 + \sqrt{3} \\ to \: find \: a + \frac{1}{a}$

By substituting appropriate values,

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

Hope it helps you!!