Question

tìm x, y thuộc Z

a, 3x=2y ; 5y=7z và 3x+5y-7z=60

b. \(\dfrac{x}{2}\) = \(\dfrac{y}{3}\)= \(\dfrac{z}{4}\) và x² + y² +z² = 116

Answer 1

\(\Rightarrow\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{7}=\dfrac{z}{5}\) và \(3x+5x-7z=60\)

\(\Rightarrow\dfrac{x}{14}=\dfrac{y}{21};\dfrac{y}{21}=\dfrac{z}{15}\) và \(3x+5x-7z=60\)

\(\Rightarrow\dfrac{x}{14}=\dfrac{y}{21}=\dfrac{z}{15}\) và \(3x+5x-7z=60\)

\(\Rightarrow\dfrac{x}{14}=\dfrac{y}{21}=\dfrac{z}{15}=\dfrac{3x+5y-7z}{3.14+5.21-7.15}=\dfrac{60}{42}=\dfrac{10}{7}\)

\(\dfrac{x}{14}=\dfrac{10}{7}\Rightarrow x=\dfrac{10}{7}.14=20\)

\(\dfrac{y}{21}=\dfrac{10}{7}\Rightarrow y=\dfrac{10}{7}.21=30\)

\(\dfrac{z}{15}=\dfrac{10}{7}\Rightarrow z=\dfrac{10}{7}.15=\dfrac{150}{7}=21,428..\approx21,438...\)