Từ \(2x=3y=-2z\Rightarrow\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{-\dfrac{1}{2}}\)
\(\Rightarrow\dfrac{2x}{1}=\dfrac{3y}{1}=\dfrac{4z}{-2}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có;
\(\dfrac{2x}{1}=\dfrac{3y}{1}=\dfrac{4z}{-2}=\dfrac{2x-3y+4z}{1-1+\left(-2\right)}=\dfrac{48}{-2}=-24\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{\dfrac{1}{2}}=-24\cdot\dfrac{1}{2}=-12\\\dfrac{y}{\dfrac{1}{3}}=-24\Rightarrow y=-24\cdot\dfrac{1}{3}=-8\\\dfrac{z}{-\dfrac{1}{2}}=-24\Rightarrow z=-24\cdot\left(-\dfrac{1}{2}\right)=12\end{matrix}\right.\)
\(2x=3y=-2z\)
\(\Rightarrow\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{-1}{2}}\)
\(\Rightarrow\dfrac{2x}{1}=\dfrac{3y}{1}=\dfrac{4z}{-2}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{2x}{1}=\dfrac{3y}{1}=\dfrac{4z}{-2}\)
\(=\dfrac{2x-3y+4z}{1-1+-2}=\dfrac{48}{-2}=-24\)
Áp dụng tính
