Question

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

Answer 1

Given :

• a = 2+√3

To find :

• a + 1/a

Solution :

$\sf \implies a = 2 + \sqrt{3}$

$\sf \implies \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3}}$

$\sf \implies \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3}} \times \dfrac{2 - \sqrt{3}}{2 - \sqrt{3}}$

$\sf \implies \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3}} \times \dfrac{2 - \sqrt{3}}{ {(2)}^{2} - {(\sqrt{3})}^{2} }$

$\sf \implies \dfrac{1}{a} = \dfrac{2 - \sqrt{3}}{ 4 - 3 }$

$\sf \implies \dfrac{1}{a} = \dfrac{2 - \sqrt{3}}{ 1 }$

$\sf \implies \dfrac{1}{a} = {2 - \sqrt{3}}$

$\sf \implies a + \dfrac{1}{a} =( 2 + \sqrt{3}) + (2 - \sqrt{3} )$

$\sf \implies a + \dfrac{1}{a} = 2 + \sqrt{3} + 2 - \sqrt{3}$

$\sf \implies a + \dfrac{1}{a} = 4$

Answer : 4