If [a + (1/a)]2 = 3 , what is the value of a3 + (1/a)3

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If [a + (1/a)]² = 3 , what is the value of a³ + (1/a)³ ?

1. 10√3/3
2. 0
3. 3√3
4. 6√3
5. None of the above

Correct Option: B

[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