Question

x/2=y/5;y/3=z/2 và 2x+3y-4z=34

Answer 1

\(\frac{x}{2}=\frac{y}{5};\frac{y}{3}=\frac{z}{2}\) và 2x + 3y - 4z = 34 

\(\frac{x}{2}=\frac{y}{5}=\frac{1}{3}.\frac{x}{2}=\frac{1}{3}.\frac{y}{5}=\frac{x}{6}=\frac{y}{15}\)

\(\frac{y}{3}=\frac{z}{2}=\frac{1}{5}.\frac{y}{3}=\frac{1}{5}.\frac{z}{2}=\frac{y}{15}=\frac{z}{10}\)

\(\Rightarrow\frac{x}{6}=\frac{y}{15}=\frac{z}{10}\) và 2x + 3y -4z = 34 

Theo tính chất dãy tỉ số bằng nhau: 

\(\frac{x}{6}=\frac{y}{15}=\frac{z}{10}\Rightarrow\frac{2x+3y-4z}{12+45-40}=\frac{34}{17}=2\)

\(\frac{x}{6}=2\Rightarrow x=2.6=12\)

\(\frac{y}{15}=2\Rightarrow y=2.15=30\)

\(\frac{z}{10}=2\Rightarrow z=2.10=20\)

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