Is there any triplets of **distinct** positive integers \((x,y,z) \) such that \( \dfrac{x^2+y^2+z^2}{x+y+z} \) and \(\dfrac{x^2+y^2+z^2}{xyz} \) are both integers?

**distinct** positive integers \((x,y,z) \) such that \( \dfrac{x^2+y^2+z^2}{x+y+z} \) and \(\dfrac{x^2+y^2+z^2}{xyz} \) are both integers?

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