Question 17
Let $a,$ $b,$ and $c$ be real numbers such that
$$
a + b + c = 2
$$ and $$
a^2 + b^2 + c^2 = 12.
$$
What is the difference between the maximum and minimum possible values of $c?$
$$
a + b + c = 2
$$ and $$
a^2 + b^2 + c^2 = 12.
$$
What is the difference between the maximum and minimum possible values of $c?$