Q1 Matemática  (Danube Competition in Mathematics 2008)

$x,y,z,t\in {\mathbb{R}}_{+}^{\ast }$: $$(xy{)}^{1/2}+(yz{)}^{1/2}+(zt{)}^{1/2}+(tx{)}^{1/2}+(xz{)}^{1/2}+(yt{)}^{1/2}\ge 3(xyz+xyt+xzt+yzt{)}^{\frac{1}{3}}$$