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

1. 1

2. -1

3. 0

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

Given,

$\Rightarrow \dfrac{x}{y} + \dfrac{y}{x} = -1 \\[1em] \Rightarrow \dfrac{x^2 + y^2}{xy} = -1 \\[1em] \Rightarrow x^2 + y^2 = -xy \\[1em] \Rightarrow x^2 + y^2 + xy = 0.$

We know that,

x³ - y³ = (x - y)(x² + y² + xy) = (x - y) × 0 = 0.

Hence, Option 3 is the correct option.