Not ordinary equations!

Geometry Level 5

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

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.


Source: HMMT
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