MathDB
Sides of triangles given by quadratic inequality

Source: Czech and Slovak Olympiad 1990, National Round, Problem 2

October 12, 2024
inequalitiesalgebratriangle inequalityparameterpositivequadratics

Problem Statement

Determine all values α∈R\alpha\in\mathbb R with the following property: if positive numbers (x,y,z)(x,y,z) satisfy the inequality x2+y2+z2≤α(xy+yz+zx),x^2+y^2+z^2\le\alpha(xy+yz+zx), then x,y,zx,y,z are sides of a triangle.
Back to ProblemsView on AoPS