MathDB

2

Part of 1989 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1989 Problem 1.2

Source: Bundeswettbewerb Mathematik 1989 Round 1

9/24/2022
A trapezoid has area 2 m22\, m^2 and the sum of its diagonals is 4 m4\,m. Determine the height of this trapezoid.
geometrytrapezoidarea
Bundeswettbewerb Mathematik 1989 Problem 2.2

Source: Bundeswettbewerb Mathematik 1989 Round 2

9/23/2022
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].
Inequalityalgebrareal numbers