Question

\(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}\)và xyz=20

Answer 1

\(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}\)

Áp dụng ................. :

 \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=\frac{x.y.z}{12.9.5}=\frac{20}{540}=\frac{1}{27}\)

Rồi tự = > x , y , z nha

 \(\frac{x}{12}=\frac{1}{27}\)

\(\frac{y}{9}=\frac{1}{27}\)

\(\frac{z}{5}=\frac{1}{27}\)

Answer 2

Ap dụng tính chất các dãy tỉ số bằng nhau, ta có:

x/12=y/9=z/5=xyz/12.9.5=20/540=1/27

=> x=1/27.12=12/27

     y=1/27.9=1/3

     z=1/27.5=5/27

Answer 3

\(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=k\)

\(\Rightarrow\hept{\begin{cases}x=12k\\y=9k\\z=5k\end{cases}}\)

\(\Rightarrow12k.9k.5k=20\)

\(\Rightarrow540k^3=20\)

\(\Rightarrow k^3=\frac{20}{540}=\frac{1}{27}\)

\(\Rightarrow k=\frac{1}{3}\)

 \(\Rightarrow\hept{\begin{cases}x=4\\y=\frac{4}{3}\\z=\frac{12}{5}\end{cases}}\)

Answer 4

Đặt: \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=k\)

\(\Rightarrow x=12k\)

\(y=9k\)

\(z=5k\)

\(\Rightarrow xyz=12k.9k.5k=540k^3=20\Rightarrow k^3=\frac{20}{540}=\frac{1}{27}=\frac{\sqrt[3]{1}}{\sqrt[3]{27}}=\frac{1}{3}\)

\(\Rightarrow x=\frac{1}{3}.12=4\)

\(y=\frac{1}{3}.9=3\)

\(z=\frac{1}{3}.5=\frac{5}{3}\)