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

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

1. 12
2. 14
3. 16
4. 18

Correct Option: B

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, a² + a^-2
= ( a + 1/a )² - 2
= ( 2 + √3 + 2 - √3)² - 2
= (4)² - 2 = 16 - 2 = 14