MathDB

7

Part of 2009 Kyrgyzstan National Olympiad

Problems(1)

Easy one

Source: Kyrgyzstan TST 2009

4/14/2009
Does a^2 \plus{} b^2 \plus{} c^2 \leqslant 2(ab \plus{} bc \plus{} ca) hold for every a,b,c a,b,c if it is known that a^4 \plus{} b^4 \plus{} c^4 \leqslant 2(a^2 b^2 \plus{} b^2 c^2 \plus{} c^2 a^2 ).
inequalitiesinequalities proposed