Trigonometric substitution perhaps?

Algebra Level 5

Given that \(x^2-y^2=2\) , find the minimum value of \({ x }^{ 2 }+4\sqrt { 3 } xy+{ 6y }^{ 2 }\) as \(x\) and \(y\) are real numbers.

Enter your answer to 3 decimal places.

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