Đặt \(\left\{{}\begin{matrix}b+c-a=x\\c+a-b=y\\a+b-c=z\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=2c\\y+z=2a\\z+x=2b\end{matrix}\right.\)
\(\Leftrightarrow P=\dfrac{2\left(y+z\right)}{x}+\dfrac{9\left(x+z\right)}{2y}+\dfrac{8\left(x+y\right)}{z}\\ \Leftrightarrow P=\dfrac{2y}{x}+\dfrac{2z}{x}+\dfrac{9x}{2y}+\dfrac{9z}{2y}+\dfrac{8x}{z}+\dfrac{8y}{z}\\ \Leftrightarrow P=\left(\dfrac{2y}{x}+\dfrac{9x}{2y}\right)+\left(\dfrac{2z}{x}+\dfrac{8x}{z}\right)+\left(\dfrac{9z}{2y}+\dfrac{8y}{z}\right)\\ \Leftrightarrow P\ge2\sqrt{\dfrac{18xy}{2xy}}+2\sqrt{\dfrac{16xz}{xz}}+2\sqrt{\dfrac{72yz}{2yz}}\\ \Leftrightarrow P\ge2\sqrt{9}+2\sqrt{16}+2\sqrt{36}=26\)
