$x+y+z=\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=xy+yz+zx\quad \text{(do xyz=1)}\\

\rightarrow (x-1)(y-1)(z-1)=xyz+x+y+z-(xy+yz+zx)-1=0\\

\rightarrow x=1\quad || \quad y=1 \quad || z=1

\Rightarrow P=0$

$x+y+z=\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=xy+yz+zx\quad \text{(do xyz=1)}\\

\rightarrow (x-1)(y-1)(z-1)=xyz+x+y+z-(xy+yz+zx)-1=0\\

\rightarrow x=1\quad || \quad y=1 \quad || z=1

\Rightarrow P=0$