Question

Cho \(\frac{40}{x-30}\)= \(\frac{20}{y-15}\)= \(\frac{28}{z-21}\) và x.y.z = 22400

TÌm x,y,z .

Answer 1

Từ đẳng thức : \(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\)

\(\Rightarrow1:\frac{40}{x-30}=1:\frac{20}{y-15}=1:\frac{28}{z-21}\)

\(\Rightarrow\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}\)

\(\Rightarrow\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)

\(\Rightarrow\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\)

Đặt \(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\Rightarrow\hept{\begin{cases}x=40k\\y=20k\\z=28k\end{cases}}\)

Khi đó : xyz = 22400

<=> 40k.20k.28k = 22400

=> 22400.k³ = 22400

=> k³ = 1

=> k³ = 1³

=> k = 1

Khi đó : x = 40.1 = 40 ; 

              y = 20.1 = 20;

              z = 28.1 = 28 

Vậy x = 40 ; y = 20 ; z = 28

Answer 2

Ta có:\(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}\)

hay\(\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}\)

\(=\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)

\(\Rightarrow\)\(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\)

\(\Rightarrow\)\(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=\frac{x.y.z}{40.20.28}=\frac{22400}{22400}=1\)

\(\Rightarrow\)\(\hept{\begin{cases}\frac{x}{40}=1\\\frac{y}{20}=1\\\frac{z}{28}=1\end{cases}}\)\(\Rightarrow\)\(\hept{\begin{cases}x=40\\y=20\\z=28\end{cases}}\)

Vậy x=40; y=20; z=28