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Algebra Level 5

Let \(x, y \) and \(z\) be real numbers such that

\[ \begin{cases} x^2 + 3xy + 3y^2 & = 25 \\ z^2 + 3yz + 3y^2 & = 169 \\ x( 2x + 3y -z ) & = 3yz. \\ \end{cases} \]

If \( xy + yz + xz \) can be expressed as \( a \sqrt{b} \), where \(a\) and \(b\) are positive integers, and \(b\) is not divisible by the square of any prime. What is the value of \(a+b\)?

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