Vì \(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}\)
Đặt \(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}=k\left(k\ne0\right)\)
\(\Rightarrow\left\{{}\begin{matrix}x=5k\\y=4k\\z=3k\end{matrix}\right.\)
\(P=\dfrac{x+2y-3z}{x-2y+3z}=\dfrac{5k+8k-9k}{5k-8k+9k}=\dfrac{5+8-9}{5-8+9}=\dfrac{4}{6}=\dfrac{2}{3}\)
⇒ \(P=\dfrac{2}{3}\)
x/5=y/4=z/3
Áp dụng tính chất dãy tỉ số bằng nhau:
x/5 = y/4 = z/3 = 2y/8 = 3z/9 = (x + 2y - 3z)/4 = (x - 2y + 3z)/6
--> P = 4/6 = 2/3
\(x:y:z=5:4:3\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}=\dfrac{2y}{8}=\dfrac{3z}{9}=\dfrac{x+2y-3z}{4}=\dfrac{x-2y+3z}{4}\\ \Rightarrow P=\dfrac{x+2y-3z}{x-2y+3z}=\dfrac{4}{4}=1\)
