MathDB

5

Part of 1990 IMO Longlists

Problems(2)

Find the minimal value of b - ILL 1990 COL1

Source:

9/18/2010
Given the condition that there exist exactly 19901990 triangles ABCABC with integral side-lengths satisfying the following conditions: (i) ∠ABC=12∠BAC;\angle ABC =\frac 12 \angle BAC; (ii) AC=b.AC = b. Find the minimal value of b.b.
geometryTrianglesanglesminimizationIMO ShortlistIMO Longlist
Fractional Inequality - ILL 1990 VIE2

Source:

9/19/2010
Let x,y,zx,y,z be positive reals and x≥y≥zx \geq y \geq z. Prove that x2yz+y2zx+z2xy≥x2+y2+z2\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y} \geq x^2+y^2+z^2
inequalitiesinequalities proposed