Why I love inequality so much

Algebra Level 5

\[\dfrac{x\sqrt{yz}}{\sqrt{x^2+1}\times \sqrt[4]{(y^2+4)(z^2+9)}}\]

Given that \( x,y\) and \(z\) are positive reals satisfying \(6x+3y+2z=xyz\), find the maximum value of the expression above.

Give your answer to two decimal place.

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