Question

If $\frac{x}{y}+\frac{y}{x}$ = -2 and x, y $\ne$ 0, then $x^3+y^3$ +3xy(x + y) is equal to:

• A. $0$
• B. $1$
• C. $-1$
• D. $-2$

Answer 1

The correct option is A $0$

Given that, $\frac{x}{y}+\frac{y}{x}=-2\Rightarrow \frac{x^2+y^2}{xy}=-2$

$x^2+y^2+2xy=0$

$(x+y{)}^2=0\Rightarrow x+y=0$.

Cubing both sides, .$x^3+y^3+3xy(x+y)=0$.

Therefore, option $A$ is correct.