# Doubtful start

Algebra Level 4

$\begin{cases} a \sqrt{b} = a+c \\ b \sqrt{c} = b+a \\ c \sqrt{a} = a+c \end{cases}$

Given that $$a,b$$ and $$c$$ are positive reals satisfying the system of equations above, find $$a+b+c$$.

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