Question 30
Find the real numbers $a$, $b$, $c$, with sum $s$, such that
$$
(\sqrt{s} - \sqrt{a})(\sqrt{s} - \sqrt{b}) + (\sqrt{s} - \sqrt{b})(\sqrt{s} - \sqrt{c}) + (\sqrt{s} - \sqrt{c})(\sqrt{s} - \sqrt{a}) = \frac{s}{2}.
$$
$$
(\sqrt{s} - \sqrt{a})(\sqrt{s} - \sqrt{b}) + (\sqrt{s} - \sqrt{b})(\sqrt{s} - \sqrt{c}) + (\sqrt{s} - \sqrt{c})(\sqrt{s} - \sqrt{a}) = \frac{s}{2}.
$$