Question

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

Answer 1

${x}^{3} + {y}^{3} = 0$

Step by step explanation:

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