A basic inequality

Algebra Level 4

\[\large \frac{x^3}{x+\sqrt{yz}}+\frac{y^3}{y+\sqrt{xz}}+\frac{z^3}{z+\sqrt{xy}}\] If \(x,y,z\) are positive reals satisfy \(x+y+z\geq 3\), find the minimum value of the expression above

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