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Part of 2001 Japan MO Finals

Problems(1)

japan 2001

Source: Titu Andreescu 2000-2001 , page 227

2/21/2004
Three nonnegative real numbers satisfy a,b,ca,b,c satisfy a2≤b2+c2,b2≤c2+a2a^2\le b^2+c^2, b^2\le c^2+a^2 and c2≤a2+b2c^2\le a^2+b^2. Prove the inequality (a+b+c)(a2+b2+c2)(a3+b3+c3)≥4(a6+b6+c6).(a+b+c)(a^2+b^2+c^2)(a^3+b^3+c^3)\ge 4(a^6+b^6+c^6). When does equality hold?
inequalitiesinequalities solvedSides of a triangle3-variable inequalitySymmetric inequalityJapan2001