Đáp án:
\[x = \dfrac{1}{2};\,\,\,\,y = - \dfrac{1}{3};\,\,\,\,z = \dfrac{1}{4}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
2x = - 3y = 4z\\
\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 3\\
\Leftrightarrow \dfrac{1}{x} + \dfrac{3}{{3y}} + \dfrac{4}{{4z}} = 3\\
\Leftrightarrow \dfrac{1}{x} + \dfrac{3}{{ - 2x}} + \dfrac{4}{{2x}} = 3\\
\Leftrightarrow \dfrac{1}{x} - \dfrac{3}{{2x}} + \dfrac{2}{x} = 3\\
\Leftrightarrow \dfrac{1}{x}.\left( {1 - \dfrac{3}{2} + 2} \right) = 3\\
\Leftrightarrow \dfrac{1}{x}.\dfrac{3}{2} = 3\\
\Leftrightarrow \dfrac{1}{x} = 2\\
\Leftrightarrow x = \dfrac{1}{2}\\
2x = - 3y = 4z \Rightarrow \left\{ \begin{array}{l}
y = - \dfrac{{2x}}{3} = - \dfrac{1}{3}\\
z = \dfrac{{2z}}{4} = \dfrac{1}{4}
\end{array} \right.
\end{array}\)
Vậy \(x = \dfrac{1}{2};\,\,\,\,y = - \dfrac{1}{3};\,\,\,\,z = \dfrac{1}{4}\)
