It's Duc Long secondary school

lam sinh to nha ban

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)}{4}=\frac{3\left(y-2\right)}{9}=\frac{2x-2}{4}=\frac{3y-6}{9}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}=\frac{\left(2x+3y-z\right)-5}{9}=\frac{50-5}{9}=\frac{45}{9}=5\) 

=> \(\frac{x-1}{2}=5\Rightarrow x=11\)

    \(\frac{y-2}{3}=5\Rightarrow y=17\)

    \(\frac{z-3}{4}=5\Rightarrow z=23\)

Vậy x = 11 ; y = 17 ; z = 23