Đặt: \(\hept{\begin{cases}b+c-a=2x\\c+a-b=2y\\a+b-c=2z\end{cases}}\Rightarrow x;y;z>0\text{ và }\hept{\begin{cases}a=y+z\\b=z+x\\c=x+y\end{cases}}\)
Áp dụng AM - GM, ta có:
\(2P=4\left(\frac{y+z}{x}\right)+9\left(\frac{x+z}{y}\right)+16\left(\frac{x+y}{z}\right)\)
\(=\left(4\frac{y}{x}+9\frac{x}{y}\right)+\left(4\frac{z}{x}+16\frac{x}{z}\right)+\left(9\frac{x}{y}+16\frac{x}{z}\right)\ge12+16+24=52\Rightarrow P\ge26\)
\(Đ\text{T}\Leftrightarrow3z=4y=6x\)