They all are squared

Algebra Level 4

{a2+ab+b2=25b2+bc+c2=49c2+ca+a2=64\large \begin{cases}a^2+ab+b^2=25 \\ b^2+bc+c^2=49 \\ c^2+ca+a^2=64\end{cases}

Let aa, bb, and cc be positive real numbers which satisfy the above system of equation. Find (a+b+c)2(a+b+c)^2.

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