cho :(3z-4y)/5=(5y-3x)/4=(4x-5z)/3 và x.x-z.z=36 Tính x,y,z

Giải thích các bước giải:

\(\begin{array}{l}
\dfrac{{3z – 4y}}{5} = \dfrac{{5y – 3x}}{4} = \dfrac{{4x – 5z}}{3}\\
 = \dfrac{{60z – 80y}}{{100}} = \dfrac{{80y – 48x}}{{64}} = \dfrac{{48x – 60z}}{{48}}\\
 = \dfrac{{60z – 80y + 80y – 48x + 48x – 60z}}{{100 + 64 + 48}}\\
 = 0\\
 \Rightarrow 3z = 4y \Rightarrow \dfrac{z}{4} = \dfrac{y}{3}\\
5y = 3x \Rightarrow \dfrac{y}{3} = \dfrac{x}{5}\\
4x = 5z \Rightarrow \dfrac{x}{5} = \dfrac{z}{4} \Rightarrow \dfrac{{{x^2}}}{{25}} = \dfrac{{{z^2}}}{{16}} = \dfrac{{{x^2} – {z^2}}}{{25 – 16}} = \dfrac{{36}}{9} = 4\\
 \Rightarrow {x^2} = 100 \Rightarrow x =  \pm 10\\
{z^2} = 64 \Rightarrow z =  \pm 8\\
 \Rightarrow y =  \pm 6
\end{array}\)