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This section has Four Questions. In each question a blank is left. Fill in the blank.
The number of real solutions $$(a, b)$$ of the equation $$\frac{a + b}{a} = \frac{b}{a + b}$$ is __________
Correct Answer: 0
We need $$a \ne 0$$ and $$a + b \ne 0$$. Cross-multiplying, $$(a + b)^2 = ab$$, i.e. $$a^2 + ab + b^2 = 0$$, which is $$\left(a + \frac{b}{2}\right)^2 + \frac{3b^2}{4} = 0$$. For real numbers this forces $$b = 0$$ and $$a = 0$$, which is not allowed. So there are 0 real solutions.
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