Tìm x,y,z [tex]\frac{5}{x-15}=\frac{3}{y-9}=\frac{7}{z-21}[/tex] và x.y.z=420
$ \frac{5}{x - 15} = \frac{3}{y - 9} = \frac{7}{z - 21} \\ \Rightarrow \frac{x - 15}{5} = \frac{y - 9}{3} = \frac{z - 21}{7} \\ \Leftrightarrow \frac{x}{5} - 3 = \frac{y}{3} - 3 = \frac{z}{7} - 3 \\ \Leftrightarrow \frac{x}{5} = \frac{y}{3} = \frac{z}{7} $
Đặt $
\frac{x}{5} = \frac{y}{3} = \frac{z}{7} = k \\ \Rightarrow x = 5k; y = 3k; z = 7k \\ xyz = 420 \\ \Rightarrow 5k . 3k . 7k = 420 \\ \Leftrightarrow 105k^3 = 420 \\ \Leftrightarrow k^3 = 4 \\ \Leftrightarrow k = \sqrt[3]{4} \\ \Rightarrow \left\{\begin{matrix}
x = 5k = 5 . \sqrt[3]{4} = \sqrt[3]{500}\\
y = 3k = 3 . \sqrt[3]{4} = \sqrt[3]{108}\\
z = 7k = 7 . \sqrt[3]{4} = \sqrt[3]{1372}
\end{matrix}\right. $
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