Có:\(\dfrac{x}{y}=\dfrac{2}{3}\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\dfrac{x}{6}=\dfrac{y}{9}\)
\(\dfrac{x}{3}=\dfrac{z}{5}\Rightarrow\dfrac{x}{6}=\dfrac{x}{10}\)
\(\Rightarrow\dfrac{x}{6}=\dfrac{y}{9}=\dfrac{z}{10}\Rightarrow\dfrac{x^2}{36}=\dfrac{y^2}{81}=\dfrac{z^2}{100}\)
và \(x^2+y^2+z^2=\dfrac{217}{4}\)
Áp dụng t/c của dãy tỉ số = nhau ta có:
\(\dfrac{x^2}{36}=\dfrac{y^2}{81}=\dfrac{z^2}{100}=\dfrac{x^2+y^2+z^2}{36+81+100}=\dfrac{217}{\dfrac{4}{217}}=\dfrac{217}{4.217}=0,25\)
\(\Rightarrow\left[{}\begin{matrix}x^2=9\\y^2=20,25\\z^2=25\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\y=4,5\\z=5\end{matrix}\right.\)
(mk chỉ lấy x,y,z t/m đề thoy)
\(\Rightarrow x+2y-2z=3+2\cdot4,5-2\cdot5=2\)
Vậy............................
