MathDB

if a^2+b^2+c^2+d^2=4 and a,b,c,d > 0 prove 2 of a,b,c,d have sum <=2

Source: Greece JBMO TST 2018 p1

April 28, 2019

algebrainequalitiesfour variables

Problem Statement

Let

a,b,c,d

be positive real numbers such that

a^2+b^2+c^2+d^2=4

. Prove that exist two of

a,b,c,d

with sum less or equal to

2