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Algebraic Identities

Question

If $\frac{x}{y} + \frac{y}{x} = - 1, (x, y \neq 0)$ , then value of $x^{3} - y^{3}$ is:
$- 1$
$1$
None of these
$0$

A

1

B

0

C

- 1

D

None of these

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Solution

Verified by Toppr

The correct option is C $0$
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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