MathDB

1

Part of 2018 Greece JBMO TST

Problems(1)

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

4/28/2019
Let a,b,c,da,b,c,d be positive real numbers such that a2+b2+c2+d2=4a^2+b^2+c^2+d^2=4. Prove that exist two of a,b,c,da,b,c,d with sum less or equal to 22.
algebrainequalitiesfour variables