Let $x,y,z$ be the positive real number such that, $x^2+xy+y^2=a^2$, $y^2+yz+z^2=b^2$ and $z^2+zx+x^2=c^2$. Find $x+y+z$.
I've been trying to solve it but the possible I get is $2(x+y+z)^2-3(xy+yz+zx)=a^2+b^2+c^2$ by summing up all the given and using $(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)$. I don't know what I should do next please help. Thank you