if a = 2 + √3, then what is the value of (a2 + a -2)?

Given that, a = 2 + √ 3
Then, 1/a = 2 - √3 [ by conjugate property ]
Conjugate law is below,
if x = p + √ q
then 1/x = p - √ q
Apply the law of algebra in above equation.
Now, we have, a ² + a ^-2
= ( a + 1/a ) ² - 2
= ( 2 + √ 3 + 2 - √ 3) ² - 2
= (4) ² - 2 = 16 - 2 = 14