Giải:
Ta có: \(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\)
\(2x=5z\Rightarrow\frac{x}{5}=\frac{z}{2}\Rightarrow\frac{x}{10}=\frac{z}{4}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{4}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{3z}{12}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{10}=\frac{y}{15}=\frac{3z}{12}=\frac{x-y+3z}{10-15+12}=\frac{3}{7}\)
+) \(\frac{x}{10}=\frac{3}{7}\Rightarrow x=\frac{30}{7}\)
+) \(\frac{y}{15}=\frac{3}{7}\Rightarrow y=\frac{45}{7}\)
+) \(\frac{z}{4}=\frac{3}{7}\Rightarrow z=\frac{12}{7}\)
Vậy bộ số \(\left(x,y,z\right)\) là \(\left(\frac{30}{7},\frac{45}{7},\frac{12}{7}\right)\)
