Question

if x/y + y/x = -1
where x,y is not equal to 0
find. x^3 - y^3​

Answer 1

$\frac{x}{y} + \frac{y}{x} = \frac{ {x}^{2} + {y}^{2} }{xy} = - 1$

${x}^{2} + {y}^{2} + xy = 0$

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

$\: \: \: \: \: \: \: \: \: = (x - y).0 \\ \: \: \: \: \: \: \: \: = 0$