\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\) hay \(\frac{x}{18}=\frac{y}{16}=\frac{z}{15}\) => \(\frac{3x}{54}=\frac{4y}{64}=\frac{5z}{75}\)
Áp dụng t/c dãy tỉ số bằng nhau ta có:
\(\frac{3x}{54}=\frac{4y}{64}=\frac{5z}{75}=\frac{3x-4y+5z}{54-64+75}=\frac{65}{65}=1\)
suy ra: \(\frac{3x}{54}=1\) => \(x=18\)
\(\frac{4y}{64}=1\) => \(y=16\)
\(\frac{5z}{75}=1\) => \(z=15\)
\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\)
\(\Leftrightarrow\frac{x}{\frac{2}{3}}=\frac{y}{\frac{3}{4}}=\frac{z}{\frac{4}{5}}\Rightarrow\frac{3x}{\frac{2}{3}.3}=\frac{4y}{\frac{3}{4}.4}=\frac{5z}{\frac{4}{5}.5}\)
\(\Leftrightarrow\frac{3x}{2}=\frac{4y}{3}=\frac{5z}{4}\)
ÁP DỤNG TÍNH CHẤT DÃY TỈ SỐ BẰNG NHAU:
\(\Leftrightarrow\frac{3x}{2}-\frac{4y}{3}+\frac{5z}{5}\Rightarrow\frac{3x-4y+5z}{2-3+5}=\frac{65}{4}\)
\(\Rightarrow\frac{3x}{2}=\frac{65}{4}\Rightarrow3x=\frac{65}{4}.2\Rightarrow3x=\frac{65}{2}\Rightarrow x=\frac{65}{6}\)
\(\Rightarrow\frac{4y}{3}=\frac{65}{4}\Rightarrow4y=\frac{65}{4}.3\Rightarrow4y=\frac{195}{4}\Rightarrow y=\frac{195}{16}\)
\(\Rightarrow\frac{5z}{5}=\frac{65}{4}\Rightarrow5z=\frac{65}{4}.5\Rightarrow5z=\frac{325}{4}\Rightarrow z=\frac{65}{4}\)
# chúc bạn học tốt #
Ta có:\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\Rightarrow\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{\frac{5}{4}}\Rightarrow\frac{3x}{\frac{9}{2}}=\frac{4y}{\frac{16}{3}}=\frac{5z}{\frac{25}{4}}\)
Áp dụng tính chất của dãy tỉ số bằng nhau:
\(\frac{3x}{\frac{9}{2}}=\frac{4y}{\frac{16}{3}}=\frac{5z}{\frac{25}{4}}=\frac{3x-4y+5z}{\frac{9}{2}-\frac{16}{3}+\frac{25}{4}}=\frac{65}{\frac{65}{12}}=65.\frac{12}{65}=12\)
\(\frac{x}{\frac{3}{2}}=12\Rightarrow x=12.\frac{3}{2}=18\)
\(\frac{y}{\frac{4}{3}}=12\Rightarrow y=12.\frac{4}{3}=16\)
\(\frac{z}{\frac{5}{4}}=12\Rightarrow z=12.\frac{5}{4}=15\)
Vậy \(x=18,y=16,z=15\)
