\(15x=-10y=6z\Leftrightarrow\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\)
\(\Leftrightarrow\frac{x}{2}=\frac{-y}{3}=\frac{1}{5}\)
Đặt \(\frac{x}{2}=\frac{-y}{3}=\frac{1}{5}=k\)
\(\Rightarrow x=2k;y=-3k;z=5k\)
\(\Rightarrow xyz=-30000\Leftrightarrow2k\cdot\left(-3\right)k\cdot5k=-30000\)
\(\Leftrightarrow-30k^3=-30000\)
\(\Leftrightarrow k^3=1000\)\(\Leftrightarrow k=10\)
\(\Rightarrow\begin{cases}x=2k=2\cdot10=20\\y=\left(-3\right)k=-3\cdot10=-30\\z=5k=5\cdot10=50\end{cases}\)
Ta có: 15x = -10y = 6z
\(=\frac{x}{\frac{1}{15}}=\frac{y}{\frac{-1}{10}}=\frac{z}{\frac{1}{6}}\)
\(\Rightarrow\left(\frac{x}{\frac{1}{15}}\right)^3=\left(\frac{y}{\frac{-1}{10}}\right)^3=\left(\frac{z}{\frac{1}{6}}\right)^3=\frac{x}{\frac{1}{15}}.\frac{y}{\frac{-1}{10}}.\frac{z}{\frac{1}{6}}\)
\(=\frac{x^3}{\frac{1}{15^3}}=\frac{y^3}{\frac{-1}{10^3}}=\frac{z^3}{\frac{1}{6^3}}=\frac{-30000}{\frac{-1}{900}}=300\)
\(\Rightarrow\begin{cases}x^3=300^3.\frac{1}{15^3}=20^3\\y^3=300^3.\frac{-1}{10^3}=-30^3\\z^3=300^3.\frac{1}{6^3}=50^3\end{cases}\)\(\Rightarrow\begin{cases}x=20\\y=-30\\z=50\end{cases}\)
Vậy x = 20; y = -30; z = 50
Ta có: 15x = -10y = 6z
\(=\frac{x}{\frac{1}{15}}=\frac{y}{\frac{-1}{10}}=\frac{z}{\frac{1}{6}}\)
\(\Rightarrow\left(\frac{x}{\frac{1}{15}}\right)^3=\left(\frac{y}{\frac{-1}{10}}\right)^3=\left(\frac{x}{\frac{1}{6}}\right)^3=\frac{x}{\frac{1}{15}}.\frac{y}{\frac{-1}{10}}.\frac{z}{\frac{1}{6}}\)
\(=\frac{x^3}{\frac{1}{15^3}}=\frac{y^3}{\frac{-1}{10^3}}=\frac{z^3}{\frac{1}{6^3}}=\frac{-30000}{\frac{1}{15}.\frac{-1}{10}.\frac{1}{6}}=\frac{-30000}{\frac{1}{900}}=-30000.900=-27000000=\left(-300\right)^3\)
\(\Rightarrow\begin{cases}x^3=\left(-300\right)^3.\frac{1}{15^3}=\left(-20\right)^3\\y^3=\left(-300\right)^3.\frac{-1}{10^3}=30^3\\z=\left(-300\right)^3.\frac{1}{6^3}=\left(-50\right)^3\end{cases}\)\(\Rightarrow\begin{cases}x=-20\\y=30\\z=-50\end{cases}\)
Vậy \(x=-20;y=30;z=-50\)
Ta có: 15x = -10y = 6z
=> 15x/30 = -10y/30 = 6z/30
=> x/2 = y/-3 = z/5
Đặt x/2 = y/-3 = z/5 = k
=> x = 2k; y = -3k; z = 5k
Thay vào: x . y . z = -30000
=> 2k . (-3k) . 5k = -30000
=> -30k^3 = -30000
=> k^3 = -30000 : (-30) = 1000
=> k = 10
=> x = 2 . 10 = 20
y = -3 . 10 = -30
z = 5 . 10 = 50
Vậy x = 20; y = -30 và z = 50.
