Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
\(\Rightarrow\frac{3\left(x-1\right)}{3.2}=\frac{4\left(y+3\right)}{4.4}=\frac{5\left(z-5\right)}{5.6}\)
\(\Rightarrow\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)
Hay: \(\frac{5z-25}{30}=\frac{3x-3}{6}=\frac{4y+12}{16}\)
Áp dụng tính châts dãy tỉ số bằng nhau ta có:
\(\frac{5z-25}{30}=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25-3x+3-4y-12}{30-6-16}=\frac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{8}=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\left\{{}\begin{matrix}\frac{5z-25}{30}=2\Rightarrow5z-25=2.30=60\Rightarrow5z=60+25=85\Rightarrow z=85:5=17\\\frac{3x-3}{6}=2\Rightarrow3x-3=2.6=12\Rightarrow3x=12+3=15\Rightarrow x=15:3=5\\\frac{4y+12}{16}=2\Rightarrow4y+12=2.16=32\Rightarrow4y=32-12=20\Rightarrow y=20:4=5\end{matrix}\right.\)
