\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)
\(\Rightarrow\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}\)\(=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{50-2-6+3}{9}\)\(=\frac{45}{9}=5\)
\(\Rightarrow\left\{\begin{matrix}2x-2=20\\3y-6=45\\z-3=20\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=11\\y=17\\z=23\end{matrix}\right.\Rightarrow x+y+z=51\)