Question

if x/y+y/x = -1 (x,y is not equal to 0 ) then x3-y3 = ?

Answer 1

$$\begin{gathered} \frac{x}{y}+\frac{y}{x}=-1 \\ \Rightarrow \frac{x^2+y^2}{xy}=-1 \\ \Rightarrow x^2+y^2=-xy.......\left(1\right) \\ \mathrm{Now}, \\ {x}^3-y^3=\left(x-y\right)\left(x^2+y^2+xy\right) \\ =\left(x-y\right)\left[-xy+xy\right]\left[\mathrm{using}\left(1\right)\right] \\ =\left(x-y\right)\left(0\right)=0 \end{gathered}$$