Question 172
Determine all triples $(a, b, c)$ of positive real numbers satisfying the following system of equations
$$
\begin{aligned}
a\sqrt{b} - c &= a, \\
b\sqrt{c} - a &= b, \\
c\sqrt{a} - b &= c.
\end{aligned}
$$
$$
\begin{aligned}
a\sqrt{b} - c &= a, \\
b\sqrt{c} - a &= b, \\
c\sqrt{a} - b &= c.
\end{aligned}
$$