3. Let $a$, $b$, and $c$ be real numbers, $k$ be a positive constant, and
$$
\left\{\begin{array}{l}
a+b+c=0, \\
a b c=k .
\end{array}\right.
$$
(1) Find the minimum value of $\max \{a, b, c\}$;
(2) Find the minimum value of $|a|+|b|+|c|$.
(提示: (1) According to the problem, $a, b, c$ must be one positive and two negative. Without loss of generality, assume $a>0, b<0, c<0$. Thus, considering $a$ as a parameter, construct a quadratic equation with $b, c$ as its two real roots. According to $\Delta \geqslant 0$, the minimum value of $\max \{a, b, c\}=a$ can be found to be $\sqrt[3]{4 k}$.
(2) From (1), we know $|a|+|b|+|c|=a-(b+c)=2 a$ has a minimum value of $2 \sqrt[3]{4 k}$.)
