An algebra problem by Dev Sharma

Algebra Level 4

\[\large \begin{cases}\begin{align} a^2 + b^2 + ab &= 9\\ b^2 + c^2 + bc &= 16\\ c^2 + a^2 + ac &= 25 \end{align}\end{cases}\]

If \(a,b,c\) satisfy the system above, find \(|ab + bc + ca|\).

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