Cho \(\left\{{}\begin{matrix}\text{x, y, z > 0}\\\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=\dfrac{1}{4}\end{matrix}\right.\). Tìm \(\min\limits_P=\dfrac{1}{\alpha\text{a}+\beta b+\gamma c}+\dfrac{1}{\beta\text{a}+\gamma b+\alpha c}+\dfrac{1}{\gamma\text{a}+\alpha b+\beta c} v\text{ới} \alpha; \beta;\text{ \gamma}\in\) \(\mathbb{N}^*\)