If $\dfrac{a}{b} + \dfrac{b}{a} = -1$ (a, b ≠ 0), then the value of a³ - b³ is :

1. $\dfrac{1}{2}$

2. 1

3. -1

4. 0

Given,

$\Rightarrow \dfrac{a}{b} + \dfrac{b}{a} = -1 \\[1em] \Rightarrow \dfrac{a^2 + b^2}{ab} = -1 \\[1em] \Rightarrow a^2 + b^2 = -ab \\[1em] \Rightarrow a^2 + b^2 + ab = 0$

Using identity,

⇒ a³ - b³ = (a - b)(a² + b² + ab)

⇒ a³ - b³ = (a - b)(0)

⇒ a³ - b³ = 0.

Hence, option 4 is correct option.