sbhatnagar
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Find \(x, \ y, \ z \ \in \mathbb{R} \) satisfying
\[\frac{4\sqrt{x^2+1}}{x}=\frac{5\sqrt{y^2+1}}{y}= \frac{6\sqrt{z^2+1}}{z} \ \ \ \text{and} \ \ \ xyz=x+y+z\]
\[\frac{4\sqrt{x^2+1}}{x}=\frac{5\sqrt{y^2+1}}{y}= \frac{6\sqrt{z^2+1}}{z} \ \ \ \text{and} \ \ \ xyz=x+y+z\]