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

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(D) Given the equation: $\frac{x}{y}+\frac{y}{x}=-1$Taking the common denominator,we get: $\frac{x^{2}+y^{2}}{x y}=-1$Multiplying both sides by $xy$,w

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$0$

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(D) Given the equation: $\frac{x}{y}+\frac{y}{x}=-1$Taking the common denominator,we get: $\frac{x^{2}+y^{2}}{x y}=-1$Multiplying both sides by $xy$,we obtain: $x^{2}+y^{2}=-x y$Rearranging the terms: $x^{2}+y^{2}+x y=0$We know the algebraic identity: $x^{3}-y^{3}=(x-y)(x^{2}+y^{2}+x y)$Substituting the value $x^{2}+y^{2}+x y=0$ into the identity:$x^{3}-y^{3}=(x-y)(0)$$x^{3}-y^{3}=0$Therefore,the correct option is $(d)$.

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

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