very easy : ) change xy + yz + zx into 1/2((x+y+z)^2-(x^2+y^2+z^2)) which simplifies into x^2+2sqrt(x)+y^2+2sqrt(y)+z^2+2sqrt(z) ≥ 9 which is trivial by AM-GM

Multiply both sides by $2$ and add $x^2+y^2+z^2$ to both sides to get \[\sum_{\text{cyc}} (x^2+2\sqrt{x}) \ge (x+y+z)^2 = 3 \sum_{\text{cyc}} x.\] However, this is just true by AM-GM. $\square$