Question

If x/ y + y /x = -1 , (x, y ≠ 0 ) find the value of x^3 – y^3

Answer 1

Answer:

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