Let $x,y,z$ be positive numbers with $x+y+z=1$. Show that $$yz+zx+xy\ge4\left(y^2z^2+z^2x^2+x^2y^2\right)+5xyz.$$When does equality hold?
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Tags: inequalities
Let $x,y,z$ be positive numbers with $x+y+z=1$. Show that $$yz+zx+xy\ge4\left(y^2z^2+z^2x^2+x^2y^2\right)+5xyz.$$When does equality hold?