If [a + (1/a)] 2 = 3 , what is the value of a 3 + (1/a) 3?

[a + (1/a)]² = 3
Taking square roots both sides, we get
a + (1/a) = √3
On cubing both sides, we
[a + (1/a)]³ = (√3)³
⇒ a³ + 1/a³ + 3.a.1/[a(a + 1/a)] = 3 √3
⇒ a³ + 1/a³ + 3√3 = 3√3
∴ a³ + 1/a³ = 0