Balancing An ABC Expression

Algebra Level 4

aa+bc+bb+ac+cc+ab\large \dfrac{a}{\sqrt{a+bc}}+\dfrac{b}{\sqrt{b+ac}}+\dfrac{c}{\sqrt{c+ab}}

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


Source: My school selection MO for grade 10.
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