Not ordinary equations!

Geometry Level 5

{a2+ab+b2=9b2+bc+c2=52c2+ca+a2=49\begin{cases} a^2+ab+b^2&=&9 \\ b^2+bc+c^2&=&52 \\ c^2+ca+a^2&=&49 \end{cases}

Let aa, bb and cc be real numbers satisfying the system of equations above.

Compute the integral value of 49b2+39bc+9c2a2\dfrac{49b^2+39bc+9c^2}{a^2}.

Hint: See the topic of this question.


Source: HMMT
×

Problem Loading...

Note Loading...

Set Loading...