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Let \(a\) and \(b\) with \(a>b>0\) be real numbers satisfying \(a^2+b^2=4ab\). Find \(\dfrac{\sqrt{a}}{\sqrt{b}} - \dfrac{\sqrt{b}}{\sqrt{a}}\).

Give your answer to 3 decimal places.

Inspiration.

This question is part of the set All-Zebra

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