Question 69
Let $a,b,c,d$ be real numbers satisfying
$$
a+b+c+d=0,\qquad a^2+b^2+c^2+d^2=12.
$$
Find the minimum and maximum possible values of $abcd$, and determine all values of $a,b,c,d$ at which these extrema are attained.
$$
a+b+c+d=0,\qquad a^2+b^2+c^2+d^2=12.
$$
Find the minimum and maximum possible values of $abcd$, and determine all values of $a,b,c,d$ at which these extrema are attained.