Question

If a = 2 + √3 , then find a^2 + 1/a^2 .

Answer 1

here is your answer
a=2+ root 3

a^2+1/a^2
(2+root 3)^2+1/(2+ root 3)^2
(4+3)+1/4+3
7+1/7
8/7
1.14

Answer 2

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

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

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

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

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

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

4 + 3 + 4√3 + 4 + 3 - 4√3

$\sf{4+3+4+3}$

$\sf{= 14}$