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Bundeswettbewerb Mathematik 1989 Problem 2.2

Source: Bundeswettbewerb Mathematik 1989 Round 2

September 23, 2022
Inequalityalgebrareal numbers

Problem Statement

Find all pairs (a,b)(a,b) of real numbers such that ∣1−x2−ax−b∣≤2−12|\sqrt{1-x^2 }-ax-b| \leq \frac{\sqrt{2} -1}{2} holds for all x∈[0,1]x\in [0,1].
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