Ta có:
$\dfrac{x}{12} = \dfrac{y}{3} = \dfrac{z}{5}$
$\Rightarrow \begin{cases}x = \dfrac{y}{3}\cdot 12 = 4y\\z = \dfrac{y}{3}\cdot 5 = \dfrac{5y}{3}\end{cases}$
Ta lại có:
$xyz = 6720$
$\Rightarrow 4y.y.\dfrac{5y}{3} = 6720$
$\Leftrightarrow \dfrac{20y^3}{3} = 6720$
$\Leftrightarrow y^3 = \dfrac{6720.3}{20} = 1008$
$\Leftrightarrow y = 2.\sqrt[3]{126}$
$\Rightarrow x = 4y = 8.\sqrt[3]{126}$
$\Rightarrow z = \dfrac{5}{3}y = \dfrac{10\sqrt[3]{126}}{3}$
