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Cubic Root Comparison (Posted on 2023-07-05) |
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Let P(x)=x3-4x2+39x-46 and Q(x)=x3+3x2+4x-3 be two polynomials.
1. Prove that each of P, Q has an unique real root. Let them be a, b respectively.
2. Prove that {a}>{b}2, where {x}=x-[x] is the fractional part of x.
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