Question

If $xy+yx=-1(x,y\ne 0)$, then find the value of $x^3–y^3$

• A. 1
• B. -1
• C. 0
• D. $\frac{1}{2}$

Answer 1

The correct option is C 0

As $\frac{x}{y}+\frac{y}{x}=-1$

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

From (i) & (ii)

$x^3-y^3=0$