[nooonuii]

82. By Cauchy-Schwarz inequality we have
$3xyz(x+y+z)\leq (xy+yz+zx)^2\leq (xy+yz+zx)(x^2+y^2+z^2).....(1)$

By AM - GM inequality we get
$\sqrt{x^2+y^2+z^2}(xy+yz+zx)\geq 3\sqrt{3}xyz......(2)$

Using equivalent forms of (1) and (2) and adding them together we get the required inequality.