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.
2026-03-28 00:29:50.1774657790
Find $xy+yz+zx$, given quadratic form of equations.
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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).