Tìm `x, y, z` biết: `a) (12x – 15y)/7 = (20z – 12x)/9 = (15y – 20z)/11`

Đáp án:

$\begin{array}{l}
\dfrac{{12x – 15y}}{7} = \dfrac{{20z – 12x}}{9} = \dfrac{{15y – 20z}}{{11}}\\
 = \dfrac{{12x – 15y + 20z – 12x + 15y – 20z}}{{7 + 9 + 11}}\\
 = \dfrac{0}{{27}} = 0\\
 \Rightarrow \left\{ \begin{array}{l}
12x = 15y\\
20z = 12x\\
15y = 20z
\end{array} \right.\\
 \Rightarrow 12x = 15y = 20z\\
 \Rightarrow \dfrac{{12x}}{{60}} = \dfrac{{15y}}{{60}} = \dfrac{{20z}}{{60}}\\
 \Rightarrow \dfrac{x}{5} = \dfrac{y}{4} = \dfrac{z}{3} = k\\
 \Rightarrow \left\{ \begin{array}{l}
x = 5k\\
y = 4k\\
z = 3k
\end{array} \right.\left( {k \in Z} \right)
\end{array}$