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The number of elements in $$\{(a, b, c) \mid a = b, (a - c)^2 = 0, a + b + c = 0, a, b, c \text{ are real numbers}\}$$ is
$$(a - c)^2 = 0$$ gives $$a = c$$, so $$a = b = c$$. Then $$a + b + c = 3a = 0$$ gives $$a = 0$$. The only element is $$(0, 0, 0)$$, so the set has 1 element.
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