Find CC

Algebra Level 4

A(32)x2+B3+2x+C=0\large A(\sqrt{3}-\sqrt{2})x^2+\frac{B}{\sqrt{3}+\sqrt{2}}x+C=0

If EE and FF are real roots of the quadratic equation above, where A=49+2064A= \sqrt [4] {49+20\sqrt{6}} and B=83+863+163+B=8\sqrt{3}+\dfrac{8\sqrt{6}}{\sqrt{3}}+\dfrac{16}{\sqrt{3}} + \cdots and that EF=(66)k\left|E-F\right|=(6\sqrt{6})^k, where k=log6(10)2log6(5)+log6log6(18)+log6(72)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 CC.

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