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The question in the OP isTitan97 said:
Given what you have found, why do you the answer is 3 instead of 6?Titan97 said:
Finding the number of rational values a function can take
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The discussion centers on determining the number of rational values that the expression f(a) + f(b) + f(c) can take, given that f(x) is continuous and differentiable, with specific conditions on its values at points a, b, and c. The participants analyze the implications of f(c) being -1.5 and the constraints that f(a) and f(b) must be irrational, leading to the conclusion that for the sum to be rational, f(a) must equal -f(b). They explore the behavior of f(x) and its derivative in the intervals [a, c] and [c, b], concluding that the values of f(a) and f(b) can only be of the form ±√I, where I is a whole number. Ultimately, they deduce that the possible combinations of f(a) and f(b) yield three distinct rational sums for f(a) + f(b) + f(c). The conversation highlights the complexity of the problem and the importance of understanding the function's behavior across its defined intervals.
- #32
Titan97
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0 - 3/2 - √2 is not a rational number
- #33
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Whoops - forgot that bit. Sorry for the noise.Titan97 said:
- #34
Titan97
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That's ok 
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