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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Posted by brandon blak on 2023-07-28 11:23:02