\(A=\frac{2a}{p-a}+\frac{9b}{2\left(p-b\right)}+\frac{8c}{p-c}=\frac{4a}{b+c-a}+\frac{9b}{a+c-b}+\frac{16c}{a+b-c}\)
Đặt \(\left\{{}\begin{matrix}a+b-c=x\\b+c-a=y\\a+c-b=z\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=\frac{x+z}{2}\\b=\frac{x+y}{2}\\c=\frac{y+z}{2}\end{matrix}\right.\)
\(\Rightarrow A=\frac{2\left(x+z\right)}{y}+\frac{9\left(x+y\right)}{2z}+\frac{8\left(y+z\right)}{x}=\frac{2x}{y}+\frac{8y}{x}+\frac{2z}{y}+\frac{9y}{2z}+\frac{9x}{2z}+\frac{8z}{x}\)
\(\Rightarrow A\ge2\sqrt{\frac{16xy}{xy}}+2\sqrt{\frac{18yz}{2yz}}+2\sqrt{\frac{72xy}{2xz}}=26\)
\(\Rightarrow A_{min}=26\) khi \(3x=6y=4z\)