Question

if x/y + y/x = -1, where x, y ≠ 0 then the value of ( x³-y³) is​

Answer 1

Step-by-step explanation:

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