Toán 7 Dãy tỉ số bằng nhau

Ta có: 3(x-1)=2(y-1)=3(z-1)[tex]\Leftrightarrow \frac{x-1}{\frac{1}{3}}=\frac{y-1}{\frac{1}{2}}=\frac{z-1}{\frac{1}{3}}\Leftrightarrow \frac{2x-2}{\frac{2}{3}}=\frac{3y-3}{\frac{3}{2}}=\frac{z-1}{\frac{1}{3}}[/tex]
Áp dụng tính chất dãy tỉ số bằng nhau:
[tex]\frac{2x-2}{\frac{2}{3}}=\frac{3y-3}{\frac{3}{2}}=\frac{z-1}{\frac{1}{3}}=\frac{2x+3y-z-2-3+1}{\frac{2}{3}+\frac{3}{2}+\frac{1}{3}}=\frac{46}{\frac{5}{2}}=\frac{92}{5}[/tex]
[tex]\Rightarrow\frac{x-1}{\frac{1}{3}}=\frac{92}{5}\Rightarrow x=\frac{107}{15}[/tex]
[tex]\Rightarrow \frac{y-1}{\frac{1}{2}}=\frac{92}{5}\Rightarrow y=\frac{51}{5}[/tex]
[tex]\Rightarrow \frac{z-1}{\frac{1}{3}}=\frac{92}{5}\Rightarrow z=\frac{107}{15}[/tex]
Vậy [tex]x=\frac{107}{15}; y=\frac{51}{5}; z=\frac{107}{15}[/tex]