Question

Tìm các số x,y,z , biết : 

a) 3x=2y; 7y=5z; x-y+z= 32

b) x-1/2=y-2/3=z-3/4 và 2x+3y-z=50

c) x/2=y/3=z/5 và xyz=810

Answer 1

a) 3x = 2y \(\Rightarrow\)\(\frac{x}{2}=\frac{y}{3}\)\(\Rightarrow\frac{x}{2}.\frac{1}{5}=\frac{y}{3}.\frac{1}{5}\)\(\Rightarrow\frac{x}{10}=\frac{y}{15}\)

\(7y=5z\Rightarrow\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{y}{5}.\frac{1}{3}=\frac{z}{7}.\frac{1}{3}\Rightarrow\frac{y}{15}=\frac{z}{15}\)

\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\Rightarrow\frac{x+y+z}{10+15+21}=\frac{32}{46}=\frac{2}{3}\)

\(\hept{\begin{cases}x=10.\frac{2}{3}=\frac{20}{3}\\y=15.\frac{2}{3}=10\\z=21.\frac{2}{3}=14\end{cases}}\)

Vậy \(\hept{\begin{cases}x=10.\frac{2}{3}=\frac{20}{3}\\y=15.\frac{2}{3}=10\\z=21.\frac{2}{3}=14\end{cases}}\)