Đáp án:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\begin{array}{l}
a)\dfrac{x}{4} = \dfrac{y}{3} = \dfrac{z}{9} = \dfrac{{3y}}{9} = \dfrac{{4z}}{{36}}\\
= \dfrac{{x - 3y - 4z}}{{4 - 9 - 36}} = \dfrac{{62}}{{ - 41}} = \dfrac{{ - 62}}{{41}}\\
\Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{ - 62}}{{41}}.4 = \dfrac{{ - 248}}{{41}}\\
y = \dfrac{{ - 62}}{{41}}.3 = \dfrac{{ - 186}}{{41}}\\
z = \dfrac{{ - 62}}{{41}}.9 = \dfrac{{ - 558}}{{41}}
\end{array} \right.\\
c)x:y:z = 4:3:2\\
\Rightarrow \dfrac{x}{4} = \dfrac{y}{3} = \dfrac{z}{2}\\
\Rightarrow {\left( {\dfrac{x}{4}} \right)^2} = {\left( {\dfrac{y}{3}} \right)^2} = {\left( {\dfrac{z}{2}} \right)^2}\\
= \dfrac{{{x^2}}}{{16}} = \dfrac{{{y^2}}}{9} = \dfrac{{{z^2}}}{4}\\
= \dfrac{{{x^2} + {y^2} - {z^2}}}{{16 + 9 - 4}} = \dfrac{{84}}{{21}} = 4\\
\Rightarrow \left\{ \begin{array}{l}
{x^2} = 4.16 = 64\\
{y^2} = 4.9 = 36\\
{z^2} = 4.4 = 16
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 8;y = 6;z = 4\\
x = - 8;y = - 6;z = - 4
\end{array} \right.
\end{array}$
