Question

if a=2+√3 find a+1/a

Answer 1

$a = 2 + \sqrt{3 } \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} \\ \frac{1}{a } = 2 - \sqrt{3}$

Now, a+1/a = 2+ root3 +2 - root3
= 4


Hope it help you

Answer 2

a = 2+√3

1/a = 1/(2+√3)

= 1/(2+√3) × (2-√3)/(2-√3)
= (2-√3)/(2²-√3²)
= (2-√3)/(4-3)
= (2-√3)/(1)
= 2 - √3

a + 1/a = 2 + √3 + (2 - √3)
= 2 + √3 + 2 - √3
= 4