Áp dụng t/c dãy tỉ số = nha ta có :

 \(\frac{x}{2}=\frac{2y}{3}=\frac{3z}{4}=\frac{x.y.z}{2.3.4}=\frac{-108}{24}=-4,5\)

\(\Rightarrow\frac{x}{2}=-4,5\Rightarrow x=-9\)

\(\Rightarrow\frac{2y}{3}=-4,5\Rightarrow y=-6,75\)

\(\Rightarrow\frac{3z}{4}=-4,5\Rightarrow z=-6\)

sai rồi

Đặt \(\frac{x}{2}=\frac{2y}{3}=\frac{3z}{4}=k\left(k\ne0\right)\)

\(\Rightarrow\hept{\begin{cases}x=2k\\2y=3k\\3z=4k\end{cases}\Rightarrow x.2y.3z=2k.3k.4k=24.k^3}\)

Ta có x.y.z=-108 suy ra x.2y.3z=-108.2.3=-648

\(\Rightarrow24.k^3=-648\Rightarrow k^3=-27\Rightarrow k=-3\)

\(\Rightarrow\hept{\begin{cases}x=-6\\2y=-9\\3z=-12\end{cases}}\Rightarrow\hept{\begin{cases}x=-6\\y=-4.5\\z=-4\end{cases}}\)

o0o I am a studious person o0o bạn làm bị sai rồi không có công thức x.y.z/e.f.g hôm trước cô mình vừa bảo xong

a) \(\frac{x}{2}=\frac{2y}{3}=\frac{3z}{4}\) và \(xyz=-108\)

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

\(\Rightarrow x=2k\)

 \(y=\frac{3}{2}k\)

\(z=\frac{4}{3}k\)

\(\Rightarrow xyz=2k.\frac{3}{2}k.\frac{4}{3}k=4k^3=-108\Rightarrow k^3=-27\Rightarrow k=\sqrt[3]{-27}=-3\)

Vậy:

\(x=2.\left(-3\right)=-6\) 

\(y=\frac{3}{2}.\left(-3\right)=-\frac{9}{2}\)

\(z=\frac{4}{3}.\left(-3\right)=-4\)

\(\frac{x}{y}=\frac{7}{20}\Leftrightarrow\frac{x}{7}=\frac{y}{20}\)

\(\frac{y}{z}=\frac{5}{8}\Leftrightarrow\frac{y}{5}=\frac{z}{8}\Leftrightarrow\frac{y}{20}=\frac{z}{32}\)

\(\Rightarrow\frac{x}{7}=\frac{y}{20}=\frac{z}{32}\) và \(3x+5y+7z=123\)

ADTCCDTSBN, ta có:

\(\frac{x}{7}=\frac{y}{20}=\frac{z}{32}=\frac{3x+5y+7z}{21+100+224}=\frac{123}{345}=\frac{41}{115}\)

\(\Rightarrow x=\frac{41}{115}.7=\frac{287}{115}\)

\(y=\frac{41}{115}.20=\frac{164}{23}\)

\(z=\frac{41}{115}.32=\frac{1312}{115}\)

-4 nha bạn

suy ra  

6xyz / 24   = xyz / 4 = 108/4 = 27

x=54

y=81/2

z=36

Nhân các vế lại với nhau :

=>6xyz / 24   = xyz / 4 = 108/4 = 27

x=54

y=81/2

z = 27x4:3=36

Vậy .................

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

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

Mà \(xyz=180\)

\(\Rightarrow2k.\frac{3k}{2}.\frac{4k}{3}=180\)

\(\Rightarrow2k.\frac{3}{2}k.\frac{4}{3}k=180\)

\(\Rightarrow k^3.4=180\)

\(\Rightarrow k^3=\frac{180}{4}=27\)

\(\Rightarrow k=\sqrt[3]{27}=3\)

\(\Rightarrow\hept{\begin{cases}x=2.3=6\\y=\frac{3.3}{2}=4,5\\z=\frac{4.3}{3}=4\end{cases}}\)

Vậy \(x=6;y=4,5;z=4\)

Ta có : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)

Áp dụng dãy tỉ số bằng nhau :

Ta có : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x+2y-3z}{2+2.3-3.4}=\frac{-20}{-4}=5\)

\(\Rightarrow x=2.5=10\)

\(\Rightarrow y=3.5=15\)

\(\Rightarrow z=4.5=20\)

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{2y}{6}=\frac{3z}{12}=\frac{x+2y-3z}{2+6-12}=\frac{-20}{-4}\)= 5

=> x = 5.2 = 10 ; y = 5.3 = 15 ; z = 5.4 = 20

Do x:2 = y:3 = z:4 =2y:6 =3z:12 =(x+2y+3z):(2+6+12)= -20:20= -1

=> x= -2 ,y= -3, z= -4