Question

[Cute phô mai que]

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

Tìm x, y, z

Answer 1

[Vũ Minh Tuấn]

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

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

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

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

Đặt \(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\Rightarrow\left\{{}\begin{matrix}x=40k\\y=20k\\z=28k\end{matrix}\right.\)

Có: \(x.y.z=22400\)

=> \(40k.20k.28k=22400\)

=> \(22400.k^3=22400\)

=> \(k^3=22400:22400\)

=> \(k^3=1\)

=> \(k=1.\)

Với \(k=1.\)

\(\Rightarrow\left\{{}\begin{matrix}x=40.1=40\\y=20.1=20\\z=28.1=28\end{matrix}\right.\)

Vậy \(\left(x;y;z\right)=\left(40;20;28\right).\)

Chúc bạn học tốt!