MathDB

2016 Algebra #10

Source:

December 24, 2016

Problem Statement

Let

a,b

and

c

be real numbers such that \begin{align*} a^2+ab+b^2&=9 \\ b^2+bc+c^2&=52 \\ c^2+ca+a^2&=49. \end{align*} Compute the value of

\dfrac{49b^2+39bc+9c^2}{a^2}