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Question

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


A
1
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B
1
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C
0
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D
12
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Solution

The correct option is C $$0$$
Given: $$\displaystyle \frac{x}{y} +\frac{y}{x} = -1$$
$$\therefore \displaystyle \frac{x^2 + y^2}{xy} = -1$$
$$x^2 + y^2 + xy =0$$...(i)
The equation, $$x^3 - y^3 = (x-y)(x^2 + xy + y^2)$$
$$x^3 -y^3 =0$$ ...... from (i)

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