Ta có:
\(\frac{x}{y}=\frac{10}{9}\Rightarrow\frac{x}{10}=\frac{y}{9}\Rightarrow\frac{x}{30}=\frac{y}{27}.\)
\(\frac{y}{z}=\frac{3}{4}\Rightarrow\frac{y}{3}=\frac{z}{4}\Rightarrow\frac{y}{27}=\frac{z}{36}.\)
\(\Rightarrow\frac{x}{30}=\frac{y}{27}=\frac{z}{36}\) và \(x-y-z=78.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{30}=\frac{y}{27}=\frac{z}{36}=\frac{x-y-z}{30-27-36}=\frac{78}{-33}=\frac{-26}{11}.\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{x}{30}=\frac{-26}{11}\Rightarrow x=\left(-\frac{26}{11}\right).30=-\frac{780}{11}\\\frac{y}{27}=\frac{-26}{11}\Rightarrow y=\left(-\frac{26}{11}\right).27=-\frac{702}{11}\\\frac{z}{36}=\frac{-26}{11}\Rightarrow z=\left(-\frac{26}{11}\right).36=-\frac{936}{11}\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(-\frac{780}{11};-\frac{702}{11};-\frac{936}{11}\right).\)
Chúc bạn học tốt!
