Question

If a=2+root3, then a square+1/a
square​

Answer 1

=> a = 2+√3 ...(1)

=> 1/a = 1/2+√3

By rationalization,

=> 1/a = 1/(2 + √3) × (2 - √3)/(2 - √3)

=> 1/a = (2 - √3)/(2 + √3)(2 - √3)

=> 1/a = (2 - √3)/(2² - √3²)

=> 1/a = 2 - √3

Now,

=> a²+1/a²

=> (2+√3)²+(2-√3)²

=> 4+3+4√3 +4+3-4√3

=> 4+3+4+3

=> 14

Hope it will help