# Find $$C$$

Algebra Level 4

$$E$$ and $$F$$ are the roots of the following quadratic equation

$A(\sqrt{3}-\sqrt{2})x^2+\frac{B}{(\sqrt{3}+\sqrt{2})}x+C=0$

where $$A= \sqrt [4] {49+20\sqrt{6}}$$ and $$B=8\sqrt{3}+\frac{8\sqrt{6}}{\sqrt{3}}+\frac{16}{\sqrt{3}} + \cdots$$

If $$\left|E-F\right|=(6\sqrt{6})^k$$, where $$k=\log _6 \left(10\right)-2\log _6\left(\sqrt{5}\right)+\log _6\sqrt{\log _6\left(18\right)+\log _6\left(72\right)}$$

Find the value of $$C$$.

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