[tex]x^2+y^2+z^2=216 \\ xy+yz+zx=230 \\ ---------- \\ x+y+z=? \\ ---------- \\ Facem~formula~(x+y+z)^2: \\ (x+y+z)^2=x^2+y^2+z^2+2xy+2xz+2yz \\ (x+y+z)^2=216+2(xy+yz+zx) \\ (x+y+z)^2=216+2*230 \\ (x+y+z)^2=216+460 \\ (x+y+z)^2=676 \\ x+y+z= \sqrt{676} \\ \boxed{x+y+z=26}[/tex]
