# The Many Faces Of An Inequality

Algebra Level 5

$\sqrt{x^2+2xy+4y^2}+\sqrt{4y^2+6yz+9z^2}+\sqrt{9z^2+3xz+x^2}$

If real numbers $$x,y,z$$ satisfy $$x+2y+3z=2\sqrt3$$, find the minimum value of the above expression.

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