Question 44
Find all $ (a, b, c) $ triplets of strictly positive reals such as $$
\left\{\begin{array}{l}
a \sqrt{b} - c = a \\
b \sqrt{c} - a = b \\
c \sqrt{a} - b = c
\end{array}\right.
$$
\left\{\begin{array}{l}
a \sqrt{b} - c = a \\
b \sqrt{c} - a = b \\
c \sqrt{a} - b = c
\end{array}\right.
$$