Ta có:\(\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3}\)Theo đề ta có:\(\frac{x}{2}=\frac{y}{3},\frac{x}{3}=\frac{y}{5}\)\(\Rightarrow\frac{1}{3}\cdot\frac{x}{2}=\frac{1}{3}\cdot\frac{y}{3},\frac{1}{2}\cdot\frac{x}{3}=\frac{1}{2}\cdot\frac{z}{5}\)\(\Rightarrow\frac{x}{6}=\frac{y}{9},\frac{x}{6}=\frac{z}{10}\)\(\Rightarrow\frac{x}{6}=\frac{y}{9}=\frac{z}{10}\)\(\Rightarrow\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}\)\(\Rightarrow\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}=\frac{x^2+y^2+z^2}{36+81+100}=\frac{217}{217}=1\)(tính chất dãy tỉ số bằng nhau)\(\Rightarrow x=\pm6,y=\pm9,z=\pm10\)Mà x,y,z là số dương\(\Rightarrow x=6,y=9,z=10\)\(\Rightarrow x+2y-2z=6+9\cdot2-10\cdot2=6+18-20=4\)Câu trả lời: Ta có:\(\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3}\)Theo đề ta có:\(\frac{x}{2}=\frac{y}{3},\frac{x}{3}=\frac{y}{5}\)\(\Rightarrow\frac{1}{3}\cdot\frac{x}{2}=\frac{1}{3}\cdot\frac{y}{3},\frac{1}{2}\cdot\frac{x}{3}=\frac{1}{2}\cdot\frac{z}{5}\)\(\Rightarrow\frac{x}{6}=\frac{y}{9},\frac{x}{6}=\frac{z}{10}\)\(\Rightarrow\frac{x}{6}=\frac{y}{9}=\frac{z}{10}\)\(\Rightarrow\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}\)\(\Rightarrow\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}=\frac{x^2+y^2+z^2}{36+81+100}=\frac{217}{217}=1\)(tính chất dãy tỉ số bằng nhau)\(\Rightarrow x=\pm6,y=\pm9,z=\pm10\)Mà x,y,z là số dương\(\Rightarrow x=6,y=9,z=10\)\(\Rightarrow x+2y-2z=6+9\cdot2-10\cdot2=6+18-20=4\)