Inspired by Nihar

Algebra Level 3

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.

This question is part of the set All-Zebra