Question

Tìm x,y,z trong cac truong hop sau

2x = 3y = 5z va  Ix-2yI=5

Answer 1

\(\left|x-2y\right|=5\Leftrightarrow x-2y=\pm5\)

\(2x=3y=5z\)

\(\Rightarrow\frac{2x}{30}=\frac{3y}{30}=\frac{5z}{30}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

TH1:\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-2y}{15-20}=\frac{-5}{-5}=1\)

\(\frac{x}{15}=1\Rightarrow x=15\);\(\frac{y}{10}=1\Rightarrow y=10\);\(\frac{z}{6}=1\Rightarrow z=6\)

TH2: \(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-2y}{15-20}=\frac{5}{-5}=-1\)

\(\frac{x}{15}=-1\Rightarrow x=-15\);\(\frac{y}{10}=-1\Rightarrow y=-10\);\(\frac{z}{6}=-1\Rightarrow z=-6\)