Here's a hint: what if you tried to glue two equilateral triangles together?

The expressions inside the radicals remind us of the Law of Cosines. For example, $\sqrt{a^2 - ab +b^2}$ can be interpreted as the length of the third side of a triangle in which two sides have lengths $a$ and $b$, and the angle between these two sides is $60^\circ$.

From these two glues triangles, what can we say about when equality occurs? When does A+B=C in a "triangle"?