Question

x/y+y/x=-1 (find x^3-y^3)

Answer 1

$\frac{x}{y} + \frac{y}{x} = - 1 \\ \frac{ {x}^{2} + {y}^{2} }{xy} = - 1 \\ {x}^{2} + {y}^{2} = - xy \\ {x}^{2} + {y}^{2} + xy = 0 \\ now \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy) \\ = (x - y) \times 0 \\ = 0$