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State True or False. If $$a$$, $$b$$ are real numbers such that $$(a - b) \colon (a + b) \colon ab = 1 \colon 5 \colon 24$$ then $$(a, b) = (12, 8)$$.
Correct Answer: True
Let $$a - b = t$$, $$a + b = 5t$$ and $$ab = 24t$$ with $$t \ne 0$$. Then $$a = 3t$$ and $$b = 2t$$, so $$6t^2 = 24t$$ and $$t = 4$$. This gives $$a = 12$$ and $$b = 8$$, so the statement is True.
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