Problem

Source: Spain Mathematical Olympiad 2021 P4

Tags: Inequality, algebra, Spain, inequalities



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