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>> $If xy + yx = - 1, (x, y \neq 0) , then val$

Question

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

A

$- 1$

B

$1$

C

$0$

D

None of these

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Solution

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Correct option is C)

if $\frac{x}{y} + \frac{y}{x} = - 1$
simplifies to $x^{2} + x y + y^{2} = 0$
as $(x^{3} - y^{3}) = (x - y) (x^{2} + x y + y^{2}) = 0$ using above result

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