Question

Tim x , y, z , biet

\(\frac{x}{3}\)=\(\frac{y}{4}\); \(\frac{y}{3}\)=\(\frac{Z}{5}\) Va 2x - 3y + z=6

Answer 1

Ta có:\(\frac{x}{3}=\frac{y}{4}\)\(\Rightarrow\frac{x}{9}=\frac{y}{12}\)

\(\frac{y}{3}=\frac{z}{5}\)\(\Rightarrow\frac{y}{12}=\frac{z}{20}\)

Suy ra:\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\)

Đặt\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}=k\)

\(\Rightarrow\hept{\begin{cases}x=9k\\y=12k\\z=20k\end{cases}}\)

Mà\(2x-3y+z=6\)

\(\Rightarrow2.9k-3.12k+20k=6\)

\(\Leftrightarrow18k-36k+20k=6\)

\(\Leftrightarrow2k=6\)

\(\Leftrightarrow k=3\)

\(\Rightarrow\hept{\begin{cases}x=3.9=27\\y=3.12=36\\z=3.20=60\end{cases}}\)(Thỏa mãn)

Vậy\(\hept{\begin{cases}x=27\\y=36\\z=60\end{cases}}\)

Linz

Answer 2

Ta có : \(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{3}=\frac{z}{5}\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{20}\end{cases}\Rightarrow\frac{x}{9}=\frac{y}{12}=\frac{z}{20}}\)

=> \(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)(dãy tỉ số bằng nhau)

=> x = 27 ; y = 36 ; z = 60

Answer 3

\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{3}=\frac{z}{5}\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{20}\end{cases}}\Leftrightarrow\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\)

Ta có \(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\Leftrightarrow\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}\)

Theo tính chất dãy tỉ số bằng nhau

\(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)

\(\hept{\begin{cases}x=9.3=27\\y=12.3=36\\z=20.3=60\end{cases}}\)

Answer 4

\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{3}=\frac{z}{5}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{3}\times\frac{1}{3}=\frac{y}{4}\times\frac{1}{3}\\\frac{y}{3}\times\frac{1}{4}=\frac{z}{5}\times\frac{1}{4}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)

\(\Rightarrow\hept{\begin{cases}x=3\times9=27\\y=3\times12=36\\z=3\times20=60\end{cases}}\)

Answer 5

Ta có :

\(\frac{x}{3}=\frac{y}{4};\frac{y}{3}=\frac{z}{5}\)

\(\Rightarrow\frac{x}{9}=\frac{y}{12};\frac{y}{12}=\frac{z}{20}\)

\(\Rightarrow\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\) 

\(\Rightarrow\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}\)  và  \(2x-3y+z=6\)

Áp dụng tính chất dãy tỉ số bằng nhau , ta có :

\(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)

\(+)\frac{x}{9}=3\Rightarrow x=27\)

\(+)\frac{y}{12}=3\Rightarrow y=36\)

\(+)\frac{z}{20}=3\Rightarrow z=60\)

Vậy x = 27 , y = 36 và z = 60 .

Học tốt nhé

Answer 6

Ta có: \(\frac{x}{3}=\frac{y}{4}\)\(\Rightarrow\)\(\frac{x}{9}=\frac{y}{12}\)

           \(\frac{y}{3}=\frac{z}{5}\)\(\Rightarrow\)\(\frac{y}{12}=\frac{z}{20}\)

    \(\Rightarrow\)\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\)

Đặt \(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}=k\)\(\left(k\ge0\right)\)

\(\Rightarrow\)\(\hept{\begin{cases}x=9k\\y=12k\\z=20k\end{cases}}\)

Ta có: \(2x-3y+z=6\)

    \(\Leftrightarrow18k-36k+20k=6\)

    \(\Leftrightarrow2k=6\)

    \(\Leftrightarrow k=3\)

  \(\Rightarrow\)\(\hept{\begin{cases}x=9.3=27\\y=12.3=36\\z=20.3=60\end{cases}}\)

Vậy \(\left(x,y,z\right)\in\left\{\left(27,36,60\right)\right\}\)