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3

Part of 1994 Greece National Olympiad

Problems(1)

(a-b)^2+(b-c)^2+(c-d)^2+(a-c)^2+(a-d)^2+(b-d)^2<= 4

Source: 1993 Greece MO p3

9/6/2024
If a2+b2+c2+d2=1a^2+b^2+c^2+d^2=1, prove that (a−b)2+(b−c)2+(c−d)2+(a−c)2+(a−d)2+(b−d)2≤4(a-b)^2+(b-c)^2+(c-d)^2+(a-c)^2+(a-d)^2+(b-d)^2\leq 4 When does equality holds?
algebrainequalities