Question 71
Let $a, b, c$ be real numbers (positive, negative, or zero) such that $a^{2}+b^{2}+c^{2}=6$.
a) Determine the maximum possible value for the expression
$$
(a-b)^{2}+(b-c)^{2}+(c-a)^{2} .
$$
b) Determine the maximum possible value for the expression
$$
(a-b)^{2} \cdot(b-c)^{2} \cdot(c-a)^{2} .
$$
In both cases, describe all the triples for which the maximum is achieved.
a) Determine the maximum possible value for the expression
$$
(a-b)^{2}+(b-c)^{2}+(c-a)^{2} .
$$
b) Determine the maximum possible value for the expression
$$
(a-b)^{2} \cdot(b-c)^{2} \cdot(c-a)^{2} .
$$
In both cases, describe all the triples for which the maximum is achieved.