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
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
\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{3}=\frac{z}{5}\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{20}\end{cases}}\Leftrightarrow\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\)
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
\(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)
\(\hept{\begin{cases}x=9.3=27\\y=12.3=36\\z=20.3=60\end{cases}}\)
\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{3}=\frac{z}{5}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{3}\times\frac{1}{3}=\frac{y}{4}\times\frac{1}{3}\\\frac{y}{3}\times\frac{1}{4}=\frac{z}{5}\times\frac{1}{4}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}\\2x-3y+z=6\end{cases}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)
\(\Rightarrow\hept{\begin{cases}x=3\times9=27\\y=3\times12=36\\z=3\times20=60\end{cases}}\)
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
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 \(\left(x,y,z\right)\in\left\{\left(27,36,60\right)\right\}\)