Question 85
Find all positive real numbers $a, b, c \leq 1$ such that
$$
\min \left\{\sqrt{\frac{a b+1}{a b c}}, \sqrt{\frac{b c+1}{a b c}}, \sqrt{\frac{a c+1}{a b c}}\right\}=\sqrt{\frac{1-a}{a}}+\sqrt{\frac{1-b}{b}}+\sqrt{\frac{1-c}{c}}
$$
$$
\min \left\{\sqrt{\frac{a b+1}{a b c}}, \sqrt{\frac{b c+1}{a b c}}, \sqrt{\frac{a c+1}{a b c}}\right\}=\sqrt{\frac{1-a}{a}}+\sqrt{\frac{1-b}{b}}+\sqrt{\frac{1-c}{c}}
$$