\(\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{6}=\frac{y}{9}\)
\(\frac{x}{z}=\frac{3}{5}\Rightarrow\frac{x}{3}=\frac{z}{5}\Rightarrow\frac{x}{6}=\frac{z}{10}\)
\(\Rightarrow\frac{x}{6}=\frac{y}{9}=\frac{z}{10}\)
\(\Rightarrow\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có :
\(\frac{x^2}{36}=\frac{y^2}{81}=\frac{z^2}{100}=\frac{x^2+y^2+z^2}{36+81+100}=\frac{21}{217}=\frac{3}{31}\)
\(\Rightarrow\hept{\begin{cases}\frac{x^2}{36}=\frac{3}{31}\\\frac{y^2}{81}=\frac{3}{31}\\\frac{z^2}{100}=\frac{3}{31}\end{cases}\Rightarrow\hept{\begin{cases}x^2=\frac{108}{31}\\y^2=\frac{243}{31}\\z^2=\frac{300}{31}\end{cases}\Rightarrow}\hept{\begin{cases}x=\left\{\pm\sqrt{\frac{108}{31}}\right\}\\y=\left\{\pm\sqrt{\frac{243}{31}}\right\}\\z=\left\{\pm\sqrt{\frac{300}{31}}\right\}\end{cases}}}\)
Vậy........
Có:\(\frac{x}{y}=\frac{2}{3}\Rightarrow3x=2y\Rightarrow\frac{3x}{12}=\frac{2y}{12}=\frac{x}{4}=\frac{y}{6}\Rightarrow\frac{x}{12}=\frac{y}{18}\left(1\right)\)
Có:\(\frac{x}{z}=\frac{3}{5}\Rightarrow5x=3z\Rightarrow\frac{5x}{15}=\frac{3z}{15}=\frac{x}{3}=\frac{z}{5}\Rightarrow\frac{x}{12}=\frac{z}{20}\left(2\right)\)
Từ (1)(2)\(\Rightarrow\frac{x}{12}=\frac{y}{18}=\frac{z}{20}\)
\(\Rightarrow\frac{x^2}{144}=\frac{y^2}{324}=\frac{z^2}{400}\)
Áp dụng tính chất dãy ti số bằng nhau ta có:
\(\frac{x^2}{144}=\frac{y^2}{324}=\frac{z^2}{400}=\frac{x^2+y^2+z^2}{144+324+400}=\frac{21}{868}=\frac{3}{124}\)
Suy ra: \(\frac{x^2}{144}=\frac{3}{124}\Rightarrow x=...\)
Tương tự tìm x,y,z.
_Học tốt_