Sửa đề: $\frac{x+3}{4}$ thành $\frac{y+3}{4}$
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Ta có: $\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}$
=> $\frac{3\left(x-1\right)}{3.2}=\frac{4\left(y+3\right)}{4.4}=\frac{5.\left(z-5\right)}{5.6}$
=> $\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}$
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}=\frac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}=\frac{5z-25-3x+3-4y-12}{8}=\frac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{8}=\frac{50-34}{8}=\frac{16}{8}=2$
$\frac{x-1}{2}=2\Rightarrow x-1=4\Rightarrow x=5$
$\frac{y+3}{4}=2\Rightarrow y+3=8\Rightarrow y=5$
$\frac{z-5}{6}=2\Rightarrow z-5=12\Rightarrow z=17$
Vậy:..........
