Question

tìm x,y,z

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

thanks các bn trc nha

 

Answer 1

suy ra  

6xyz / 24   = xyz / 4 = 108/4 = 27

x=54

y=81/2

z=36

Answer 2

Nhân các vế lại với nhau :

=>6xyz / 24   = xyz / 4 = 108/4 = 27

x=54

y=81/2

z = 27x4:3=36

Vậy .................

Answer 3

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 \(x=6;y=4,5;z=4\)