MathDB

Inequality

Source: 2010 IrMO Paper 1 Problem 3

January 30, 2018

inequalities

Problem Statement

Suppose

x,y,z

are positive numbers such that

x+y+z=1

. Prove that (a)

xy+yz+xz\ge 9xyz

; (b)

xy+yz+xz<\frac{1}{4}+3xyz

;