\(12x=15y=28z\)

\(\Rightarrow\dfrac{x}{35}=\dfrac{y}{28}=\dfrac{z}{15}\)

\(\Rightarrow\dfrac{x^3}{35^3}=\dfrac{y^3}{28^3}=\dfrac{z^3}{15^3}=\dfrac{xyz}{35.28.15}=\dfrac{14700}{14700}=1\)

\(\Rightarrow\left\{{}\begin{matrix}x=35\\y=28\\z=15\end{matrix}\right.\)

\(12x=15y=28z\Rightarrow\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{28}}\)

Đặt \(\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{28}}=k\Rightarrow x=\dfrac{1}{12}k;y=\dfrac{1}{15}k;z=\dfrac{1}{28}k\)

\(xyz=14700\\ \Rightarrow\dfrac{1}{12}k\cdot\dfrac{1}{15}k\cdot\dfrac{1}{28}k=14700\\ \Rightarrow\dfrac{1}{5040}k^3=14700\\ \Rightarrow k^3=74088000\\ \Rightarrow k=420\\ \Rightarrow\left\{{}\begin{matrix}x=35\\y=28\\z=15\end{matrix}\right.\)

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\)  => 

b) Đặt \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=k\)

\(\Rightarrow x=12k,y=9k,z=5k\)

\(xyz=20\)

\(\Rightarrow12k.9k.5k=20\)

\(\Rightarrow540k^3=20\)

\(\Rightarrow k^3=\frac{1}{27}\)

\(\Rightarrow k=\frac{1}{3}\)

Khi   \(k=\frac{1}{3}\)

\(\Rightarrow\frac{x}{12}=\frac{1}{3}\Rightarrow x=4\)

\(\frac{y}{9}=\frac{1}{3}\Rightarrow y=3\)

\(\frac{z}{5}=\frac{1}{3}\Rightarrow z=\frac{5}{3}\)

Vậy x = ..... ; y = ............ ; z = .............

\(\frac{12x-5y}{7}=\frac{20z-12x}{9}=\frac{15y-20z}{11}=\frac{12x-15y+20z-12x+15y-20x}{7+9+11}=0\)\(=0\)

=> 12x - 15y =0

=> 12x = 15y

=> \(\frac{x}{15}=\frac{y}{12}\)

=> \(\frac{x}{60}=\frac{y}{48}\)

20z - 12x = 0 

=> 20z = 12x 

=> \(\frac{x}{20}=\frac{z}{12}\)

=> \(\frac{x}{60}=\frac{z}{36}\)

=> \(\frac{x}{60}=\frac{y}{48}=\frac{z}{36}=\frac{x+y+z}{60+48+36}=\frac{48}{144}=\frac{1}{3}\)

=> x = 1 . 60 : 3 = 20

y = 1 . 48 : 3 = 16

z = 1 . 36 : 3 = 12