Giúp mik câu cuối với ạ

\(P=\dfrac{2x+y+z}{2(y+z)}.\dfrac{2y+x+z}{2(z+x)}.\dfrac{2z+x+y}{2(x+y)}\\P=\dfrac{[(x+y)(x+z)][(x+y)+(y+z)][(y+z)+(z+x)]}{(x+y)(y+z)(z+x)}\ge\dfrac{2\sqrt{(x+y)(x+z)}.2\sqrt{(x+y)(y+z)}.2\sqrt{(y+z)(z+x)}}{8(x+y)(y+z)(z+x)}=1\\\Rightarrow min_P=1\Leftrightarrow x=y=z\)