Question

If x/y + y/x = -1 where x ≠ 0 and y ≠ 0 then find the value of x³ – y³

Answer 1

Dear Student,

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

Regards