If frac{x}{y}+frac{y}{x}=-1(x, y neq 0), the | vedclass

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Question

$\frac{x}{y}+\frac{y}{x}=-1 \Rightarrow \frac{x^{2}+y^{2}}{x y}=-1$

$\Rightarrow \quad x^{2}+y^{2}=-x y$

Now, $x^{3}-y^{3}=(x-y)\left(x^{2}+y^{2

Vedclass · Accepted Answer

$0$

Vedclass · Answer

$\frac{x}{y}+\frac{y}{x}=-1 \Rightarrow \frac{x^{2}+y^{2}}{x y}=-1$

$\Rightarrow \quad x^{2}+y^{2}=-x y$

Now, $x^{3}-y^{3}=(x-y)\left(x^{2}+y^{2}+x y\right)$

$=(x-y)(-x y+x y) \quad\left[\because x^{2}+y^{2}=-x y\right]$

$=(x-y)(0)$

$=0$

Hence, $(d)$ is the correct answer.

If $\frac{x}{y}+\frac{y}{x}=-1(x, y \neq 0),$ the value of $x^{3}-y^{3}$ is

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