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min/max of abcd with a+b+c+d=0 and a^2+b^2+c^2+d^2=12

Source: Spain Mathematical Olympiad 2021 P4

May 10, 2021
InequalityalgebraSpaininequalities

Problem Statement

Let a,b,c,da,b,c,d real numbers such that:
a+b+c+d=0 and a2+b2+c2+d2=12 a+b+c+d=0 \text{ and } a^2+b^2+c^2+d^2 = 12
Find the minimum and maximum possible values for abcdabcd, and determine for which values of a,b,c,da,b,c,d the minimum and maximum are attained.
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