If $\dfrac{x}{y} + \dfrac{y}{x}$ = -1 (x ≠ 0, y ≠ 0), then the value of x³ - y³ is

1. 1

2. -1

3. 0

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

Given,

$\Rightarrow \dfrac{x}{y} + \dfrac{y}{x} = -1\\[1em] \Rightarrow \dfrac{x^2}{xy} + \dfrac{y^2}{xy} = -1\\[1em] \Rightarrow \dfrac{x^2 + y^2}{xy} = -1\\[1em] \Rightarrow x^2 + y^2 = -xy …………..(1)$

We know that,

x³ - y³ = (x - y)(x² + xy + y²)

Substituting the value of x² + y² in above equation, we get

⇒ x³ - y³ = (x - y)(-xy + xy)

⇒ x³ - y³ = (x - y) × 0 = 0.

Hence, option 3 is the correct option.