# Rooted away

Algebra Level 4

$$x$$ is a real number that satisfies the equation

$x = \sqrt{4-x}\sqrt{5-x} + \sqrt{5-x}\sqrt{6-x} + \sqrt{6-x}\sqrt{4-x}.$

If $$x$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, what is $$a+b$$?

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