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Prove that there is a positive number c such that square c = 2
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Is this for an abstract algebra class?
No calculus 1 Hint: use intermediate value theorem
I think the point is to show that the function: \[f(x) = x^2 -2\] has a zero
Because, for instance, when x=1, the function is less than zero and when x=2, the function is greater than zero. So, via IVT there is at least one point where the function equals zero.
Also, your answer may entail proving that said function is CONTINUOUS... make sense?
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