# Milk It

Algebra Level pending

The following inequality holds itself true for all positive reals $$x,y,z$$.

$xy(x+y) + xz(x+z) + yz(y+z) \geq C \cdot xyz$

Evaluate the greatest possible value of the constant $$C$$.

Be sure to include in your answer the procedure used to check the inequality and its equality case. This question is not original.

×