\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)}{4}=\frac{3\left(y-2\right)}{9}=\frac{2x-2}{4}=\frac{3y-6}{9}\)
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
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\Rightarrow\frac{2x-1}{4}=\frac{3y-2}{9}=\frac{z-3}{4}\) vaf 2x+3y-z=50
Ap dung tinh chat day ti so bang nhau , ta co :
\(\frac{2x-1}{4}=\frac{3y-2}{9}=\frac{z-3}{4}=\frac{2x+3y-z-1-2-3}{4+9-4}=\frac{50-\left(-4\right)}{9}=-\frac{54}{9}=-6\)
Suy ra : \(\frac{2x-1}{4}=-6\Rightarrow2x-1=-6.4=-24\Rightarrow x-1=-24:2=-12\Rightarrow x=-12+1=-11\)
\(\frac{3y-2}{9}=-6\Rightarrow3y-2=-6.9=-54\Rightarrow y-2=-54:3=-18\Rightarrow y=-18+\left(-2\right)=-20\)
\(\frac{z-3}{4}\Rightarrow z-3=4.3=12\Rightarrow z=12+3=15\)
ai tick cho tui với, tui tick lại cho !
