Đáp án:
$\left\{\begin{matrix}x=505.3=1515& \\y=505.4=2020&\\z=505.5=2525& \end{matrix}\right.$
Giải thích các bước giải:
`(4x-3y)/5=(5y-4z)/3=(3z-5x)/4`
`=> (20x-15y)/25=(15y-12z)/9=(12z-20x)/16`
`=(20x-15y+15y-12z+12z-20x)/(25+9+16)=0/50=0`
`=>` $\left\{\begin{matrix}\dfrac{4x-3y}{5}=0& \\\dfrac{5y-4z}{3}=0&\\\dfrac{3z-5x}{4}=0& \end{matrix}\right.$ `=>` $\left\{\begin{matrix}4x-3y=0& \\5y-4z=0&\\3z-5x=0& \end{matrix}\right.$ `=>` $\left\{\begin{matrix}4x=3y& \\5y=4z&\\3z=5x& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}\dfrac{x}{3}=\dfrac{y}{4}& \\\dfrac{y}{4}=\dfrac{z}{5}&\\\dfrac{z}{5}=\dfrac{x}{3}& \end{matrix}\right.$ `=> x/3=y/4=z/5`
`=(x-y+z)/(3-4+5)=2020/4=505`
`=>` $\left\{\begin{matrix}x=505.3=1515& \\y=505.4=2020&\\z=505.5=2525& \end{matrix}\right.$
