Correct Option: D

Given equation is,
a + 1/a = √3 .............................(i)
On squaring both sides
⇒ a² + 1/a² + 2 = 3
⇒ a² + 1/a² = 1 ..............................(ii)

Now, multiplying Equation (i) and (ii), we get
(a + 1/a) (a² + 1/a²) = √3
⇒ a³ + a/a² + a²/a + 1/a³ = √3
⇒ a³ + 1/a³ + ( a + 1/a ) = √3
now put the value of a + 1/a in above equation,
⇒ a³ + 1/a³ + √3 = √3 [from Eq. (i)]
⇒ a³ + 1/a³ = 0
⇒ ( a⁶ + 1 ) /a³ = 0
⇒ a⁶ + 1 = 0 x a³
⇒ a⁶ + 1 = 0
⇒ a⁶ = -1
∴ a⁶ - 1/a⁶ + 2
put the value of a⁶
= (-1)⁶ - 1/(-1)⁶ + 2
= 1 - 1 + 2 = 2