Linh Moi

Đổi biến: $(a,b,c) \rightarrow (xy,yz,zx)$

$\Rightarrow \frac{x-y}{z+y}+\frac{3y+z}{x+z}+\frac{2z-2y}{x+y}$

Đổi biến: $(m,n,p) \rightarrow (z+y,x+z,x+y) \Rightarrow 2x=n+p-m; 2y+m+p-n;2z=m+n-p$

$\Rightarrow P=\left ( \frac{n}{m}+\frac{2m}{n} \right )+\left ( \frac{p}{n}+\frac{2n}{p} \right )-4 \geq_{AM-GM}2\sqrt{\frac{n}{m}.\frac{2m}{n}}+2\sqrt{\frac{p}{n}.\frac{2n}{p}}-4=-4+4\sqrt{2}$

$\Rightarrow P_{min}=-4+4\sqrt{2}$ khi $(a,b,c)=(1,1+2\sqrt{2},-5+4\sqrt{2})$

anh tìm dấu = kiểu j vậy ạ ?