Identical Deformation With Radicals

Algebra Level 5

\[x^{2}-\frac{1}{x^{2}}\]

\( x\) is a value that satisfies \(\sqrt{x}-\frac{1}{\sqrt{x}}=-2\). When substituted into the above expression, we obtain the value \(a\sqrt{b}\), where \(a\) and \(b\) are integers with \(b\) square-free. Find \(|a+b|\).

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