Is this hard? I think I remember Pythagoras!

Algebra Level 5

\[ \left | \sqrt{x^2+4y^2-4xy - 4y + 2x+2} - \sqrt{x^2+4z^2 - 4xz - 4z + 2x+17} \right | \]

Given that \(2x+y+3z=6\) and \(x+y+z=2\), find the maximum value of the expression above.

Bonus: Are the values dependent on the variables? Which one?

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