Question

If
$\frac{x}{y} + \frac{y}{x } = - 1$
(where x and y not equal to zero)then find the value of
${x}^{3} - {y}^{3}$
​

Answer 1

x/y+y/x= -1

By taking out lcm,

x²+y²/xy = -1

x²+y²= -xy

Thus, x²+y²+xy=0

We know that, x³-y³=(x-y)(x²+y²+xy)

x³-y³=(x-y)0

x³-y³=0