A geometry problem by Aditya Moger

Geometry Level 3

\[ \large \dfrac x{\sqrt{1+x^2}} + \dfrac y{\sqrt{1+y^2}} + \dfrac z{\sqrt{1+z^2}} \leq \dfrac{3\sqrt3}2 \]

If \(x,y\) and \(z\) are real numbers such that \(x + y + z = xyz\), then is the inequality above correct?

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