Find $xy+yz+zx$, given quadratic form of equations. Given that $(x,y,z) \in \mathbb R^+$ and the following equations:
$$x^2 + y^2 + xy = 1,$$
$$y^2 + z^2 + yz = 2,$$
$$z^2 + x^2 + xz = 3.$$
How to find $xy + yz + zx$? Please help.

Consider a triangle ABC. 
         take a point inside triangle say O. such that sides subtend angle of 2π/3 each.
let OA = x, OB = y, OC = z.
So sides will come out 1, √2, √3. ( cosine rule ).
as triangle is right angled, area  = 1/2*√2
Also add up area of triangle formed by smaller ones we get,
       xy + yz + zx = √(8/3).
