Star Tau Ceti: Understanding the Rising Interest Behind the Species

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But as written, the only logical conclusion is that $ a = 0 $, and $ b $ is arbitrary. But since the question expects a boxed answer, and in olympiad problems, sometimes such equations imply identities.
Another idea: suppose the equation holds for all $ x $, but here its for a single variable.
Given the ambiguity, but to provide an answer, perhaps the intended solution assumes $ a

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