Question

Tìm \(x,y,z\) bằng 2 cách biết: \(\dfrac{x}{2}\) = \(\dfrac{2y}{3}\) = \(\dfrac{3z}{4}\) và \(xyz\) = -108

Answer 1

Đặt \(\dfrac{x}{2}=\dfrac{2y}{3}=\dfrac{3z}{4}=k\Rightarrow x=2k;y=\dfrac{3k}{2};z=\dfrac{4k}{3}\)

Khi đó \(xyz=-108\Leftrightarrow2k\cdot\dfrac{3k}{2}\cdot\dfrac{4k}{3}=-108\)

\(\dfrac{24k^3}{6}=-108\Leftrightarrow4k^3=-108\)

\(\Leftrightarrow k^3=-27\Rightarrow k=-3\)

\(\Rightarrow\left\{{}\begin{matrix}x=2k=2\cdot\left(-3\right)=-6\\y=\dfrac{3k}{2}=\dfrac{3\cdot\left(-3\right)}{2}=-\dfrac{9}{2}\\z=\dfrac{4k}{3}=\dfrac{4\cdot\left(-3\right)}{3}=-4\end{matrix}\right.\)