# 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.

×