Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=k\Rightarrow\hept{\begin{cases}x=2k\\y=3k\\z=4k\end{cases}}\)

\(\Rightarrow xyz=2k\cdot3k\cdot4k=24k^3=192\)

\(\Rightarrow k^3=8=2^3\)

\(\Rightarrow k=2\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=2\\\frac{y}{3}=2\\\frac{z}{4}=2\end{cases}}\Rightarrow\hept{\begin{cases}x=4\\y=6\\z=8\end{cases}}\)

Vậy x = 4; y = 6; z = 8

Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=k\Rightarrow x=2k;y=3k;z=4k\)

\(xyz=192\Rightarrow24k^3=192\Rightarrow k^3=8\Rightarrow k=2\)

\(\Rightarrow x=2.2=4\)

\(y=2.3=6\)

\(z=2.4=8\)

bài 1 : a,ta có 3/x-1 =4/y-2=5/z-3 =>  x-1/3=y-2/4=z-3/5 

áp dụng .... => x-1+y-2+z-3 / 3+4+5 = x+y+z-1-2-3/3+4+5 = 12/12=1

do x-1/3 = 1 => x-1 = 3 => x= 4 ( tìm y,z tương tự

Bài 1: 

a) Ta có: 3/x - 1 = 4/y - 2 = 5/z - 3 => x - 1/3 = y - 2/4 = z - 3/5 áp dụng ... =>x - 1 + y - 2 + z - 3/3 + 4 + 5 = x + y + z - 1 - 2 - 3/3 + 4 + 5 = 12/12 = 1 do x - 1/3 = 1 => x - 1 = 3 => x = 4 ( tìm y, z tương tự )

cũng dễ thôi

\(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\)

\(\Leftrightarrow\dfrac{x-1}{3}=\dfrac{y-2}{4}=\dfrac{z-3}{5}=k\)

=>x-1=3k; y-2=4k; z-3=5k

=>x=3k+1;y=4k+3;z=5k+3

xyz=192

=>(3k+1)(4k+3)(5k+3)=192

=>(12k^2+13k+3)(5k+3)=192

=>60k^3+36k^2+65k^2+39k+15k+9=192

=>60k^3+101k^2+54k-183=0

=>k=0,92

=>x=3k+1=3,76; y=4k+3=6,68; z=7,6

ta có ........= x-1/3 ........ ( đảo ngược  lại)  =k

=> x-1 =3k=> x = 3k+1

y-2 = 4k=> y =4k+2

z-3=5k=> z = 5k+3

=> xyz = 3k+1. 4k+2.5k+3= 192 .  (1+2+3) =.....

=> tự tính nha bn

Đặt \(\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-3}{5}=k\) ( đảo ngược )

\(\Rightarrow x-1=3k;y-2=4k;z-3=5k\)

\(\Rightarrow x=3k+1;y=4k+2;z=5k+3\)

\(\Rightarrow xyz=192\Leftrightarrow\left(3k+1\right)\left(4k+2\right)\left(5k+3\right)=192\Leftrightarrow k=1\)

Suy ra : 

+) \(x-1=3k\Leftrightarrow x-1=3\Leftrightarrow x=4\)

+) \(y-2=4k\Leftrightarrow y-2=4\Leftrightarrow y=6\)

+) \(z-3=5k\Leftrightarrow z-3=5\Leftrightarrow z=8\)

Vậy x = 4 ; y = 6 ; z = 8