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Question

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


A
0
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B
1
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C
1
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D
2
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Solution

The correct option is A $$0$$
Given that, $$\cfrac{x}{y} + \cfrac{y}{x} = -2 \Rightarrow \cfrac{x^2 + y^2}{xy} = -2$$
 $$x^2 + y^2+ 2xy = 0$$
$$(x + y)^2 = 0 \Rightarrow x + y = 0$$.
Cubing both sides, .$$x^3 +y^3 + 3xy (x + y) = 0$$.
Therefore, option $$A$$ is correct.

Mathematics

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