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Question 8

$$x$$ and $$y$$ are real numbers which satisfy $$x^2 + y^2 + 2x + 6y + 10 = 0$$. Then the numerical value of $$\frac{x + y}{x - y}$$ is

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Completing squares gives $$(x + 1)^2 + (y + 3)^2 = 0$$, and a sum of two real squares vanishes only when each is zero. Hence $$x = -1$$ and $$y = -3$$. Then $$\frac{x + y}{x - y} = \frac{-4}{2} = -2$$.

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