# Its beautiful (Just observe it)

Algebra Level 5

$\begin{cases} 4\dfrac{\sqrt{x^{2} + 1}}{x} = 5\dfrac{\sqrt{y^{2} + 1}}{y}=6\dfrac{\sqrt{z^{2} + 1}}{z} \\ xyz = x + y + z\end{cases}$

If $$x = \dfrac{\sqrt{a}}{b} , y = c\dfrac{\sqrt{d}}{e} , z = f\sqrt{g}$$ satisfy the above system of equations, then find $$(a + b + \ldots + g )$$.

• The expression is in simplest terms, meaning that all of the variables are positive integers, $$a, d, g$$ are square free and $$c, e$$ are coprime.
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