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Function problem

Source: China South East Mathematical Olympiad2011

August 18, 2011
functioncalculusderivativealgebra proposedalgebra

Problem Statement

If min⁡{ax2+bx2+1∣x∈R}=3\min \left \{ \frac{ax^2+b}{\sqrt{x^2+1}} \mid x \in \mathbb{R}\right \} = 3, then (1) Find the range of bb; (2) for every given bb, find aa.
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