Explanation

(b)
Let $\mathrm{\Delta} = \left| \begin{array}{r}
a\ \ 1\ \ 1 \\
1\ \ b\ \ 1 \\
1\ \ 1\ \ c
\end{array} \right| = abc - (a + b + c) + 2$
$\because\mathrm{\Delta} > 0 \Rightarrow abc + 2 > a + b + c$
$\Rightarrow abc + 2 > 3(abc)^{1/3}$
$\left\lbrack \because AM > GM \Rightarrow \frac{a + b + c}{0} > (abc)^{1/3} \right\rbrack$
$\Rightarrow x^{3} + 2 > 3x,\ where\ x = (abc)^{1/3}$
$\Rightarrow x^{3} - 3x + 2 > 0 \Rightarrow (x - 1)^{2}(x + 2) > 0$
$\Rightarrow x + 2 > 0 \Rightarrow x > - 2 \Rightarrow (abc)^{1/3} > - 2$
$\Rightarrow abc > - 8$