Question

 xla2 + yla2 + zla2 =216
xy+yz+zx=230
calculati     x+y+z =?

Answer 1

(x+y+z)²=(x²+y²+z²)+(2xy+2xz+2yz)=
            =216+2(xy+xz+yz)=
            =216+2*230=
             =216+460=676
x+y+z=√676=26

Answer 2

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