If a 2 + b 2 = a, then the value of a 12 + a 6 + 1 is?

a² + 1 = a ⇒ a + 1/a = 1
On squaring both sides, we get
a² + 1/a² + 2 = 1
⇒ a² + 1/a² = -1
On cubing both sides, we get
(a² + 1/a²)³ = (-1)³
⇒ a⁶ + 1/a⁶ + 3a² x 1/a²(a² + 1/a²) = -1
⇒ a⁶ + 1/a⁶ + 3 x (-1) = -1
Now, a⁶ + 1/a⁶ + 1 = 3
As, a¹² + a⁶ + 1 can also be written as a⁶ + 1/a⁶ + 1
∴ a¹² + a⁶ + 1 = 3