Question

If `(a + 1/a)^2` = 3, then the value of `a^3 + 1/a^3` is

Options

• 0

• 9

• `3sqrt(3)`

• `sqrt(3)`

Answer 1

0

Explanation:

`(a + 1/a)^2` = 3

∴ `a + 1/a = sqrt(3)`

On cubing,

`a^3 + 1/a^3 + 3(a + 1/a) = 3sqrt(3)`

⇒ `a^3 + 1/a^3 + 3sqrt(3) = 3sqrt(3)`

⇒ `a^3 + 1/a^3` = 0