# Balancing An ABC Expression

Algebra Level 4

$\large \dfrac{a}{\sqrt{a+bc}}+\dfrac{b}{\sqrt{b+ac}}+\dfrac{c}{\sqrt{c+ab}}$

Let $$a,b$$ and $$c$$ be positive reals satisfying $$a+b+c=1$$. Find the maximum value of the expression above.

###### Source: My school selection MO for grade 10.
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