IMO 1987 LL USS67

If a, b, c, d are real numbers such that a2 + b2 + c2 + d2 \leq1,

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IMO 1987 LL USS67

Origin: USS

Problem

If a, b, c, d are real numbers such that a2 + b2 + c2 + d2 \leq1, find the maximum of the expression (a + b)4 + (a + c)4 + (a + d)4 + (b + c)4 + (b + d)4 + (c + d)4.