# What is there to do

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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