Olympiad Problem 1

Algebra Level 5

Let x,y,z be positive reals for which:

\(\sum (xy)^{2}=6xyz\)

Find the minimum value of:

\(\sum \sqrt{\frac{x}{x+yz}}\)

If the minimum value can be expressed in the form a\(\sqrt{b}\) + c, then find a + b + c

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