Advanced Number Theory · Superchallenge problem

Positive real numbers $x$, $y$, $z$ satisfy $x^2+xy+y^2=9$, $y^2+yz+z^2=16$, and $z^2+zx+x^2=25$. Then $xy+yz+zx=a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is squarefree. Find $a+b$.