$\begin{cases} a^2+ab+b^2&=&9 \\ b^2+bc+c^2&=&52 \\ c^2+ca+a^2&=&49 \end{cases}$

Let $a$, $b$ and $c$ be real numbers satisfying the system of equations above.

Compute the integral value of $\dfrac{49b^2+39bc+9c^2}{a^2}$.

**Hint**: See the topic of this question.