MathDB
Inequality with unknown parameters

Source: Czech and Slovak Olympiad 1978, National Round, Problem 2

October 11, 2024
inequalitiesalgebraparameterization

Problem Statement

Determine (at least one) pair of real numbers k,qk,q such that the inequality 2∣1−x2−kx−q∣≤2−12\left|\sqrt{1-x^2}-kx-q\right|\le\sqrt2-1 holds for all x∈[0,1].x\in[0,1].
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