Question

\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\)   và x.y =1200

Answer 1

\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\Rightarrow\frac{x-9}{y-12}\)

\(\Rightarrow\frac{3}{4}=\frac{x-9}{y-12}=\frac{9}{12}=\frac{x-9}{y-12}=\frac{x-9+9}{y-12+12}\)\(=\frac{x}{y}=\frac{xy}{y^2}=\frac{x^2}{xy}\)

Từ \(\frac{3}{4}=\frac{xy}{y^2}\Rightarrow\frac{3}{4}=\frac{1200}{y^2}\Rightarrow y^2=1200\cdot\frac{4}{3}=20^2\Rightarrow y=\pm40\)

Nếu y=40 => x= 1200: 40 = 30 

Mà \(\frac{15}{x-9}=\frac{40}{z-24}\Rightarrow z=80\)

Nếu y = -40 => x = 1200:(-40) = - 30 

Mà \(\frac{15}{x-9}=\frac{40}{z-24}\Rightarrow z=-80\)

Vây (x , y , z ) = ( 30, 40, 80); ( - 30; -40; -80)