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x:y:z=5:4:3
=>x/5=y/4=z/3
theo t/c dãy tỉ số= nhau:
\(\frac{x+2y-3z}{5+2.4-3.3}=\frac{x-2y+3z}{5-2.4+3.3}\Rightarrow\frac{x+2y-3z}{4}=\frac{x-2y+3z}{6}\Rightarrow\frac{x+2y-3z}{x-2y+3z}=\frac{4}{6}=\frac{2}{3}\)
=>P+1/3=2/3+1/3=3/3=1
vậy P=1
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài `10`
`a,` Ta có : `x/2=y/3=>(4x)/8 =(3y)/9`
ADTC dãy tỉ số bằng nhau ta có :
`(4x)/8 =(3y)/9=(4x-3y)/(8-9)=(-2)/(-1)=2`
`=> x/2=2=>x=2.2=4`
`=>y/3=2=>y=2.3=6`
`b,` Ta có : `2x=5y=>x/5=y/2`
ADTC dãy tỉ số bằng nhau ta có :
`x/5=y/2=(x+y)/(5+2)=-42/7=-6`
`=>x/5=-6=>x=-6.5=-30`
`=>y/2=-6=>y=-6.2=-12`
Bài `11`
`a,` Ta có : `x/3=y/4=z/6=>x/3=(2y)/8 =(3z)/18`
ADTC dãy tỉ số bằng nhau ta có :
`x/3=(2y)/8=(3z)/18=(x+2y-3z)/(3+8-18)=(-14)/(-7)=2`
`=>x/3=2=>x=2.3=6`
`=>y/4=2=>y=2.4=8`
`=>z/6=2=>z=2.6=12`
Bạn đăng lại `2` câu sau nhe , mình ko hiểu `x=y-z` với `15x-5y=3x=45`
`d,` Ta có :
`x/2=y/3=>x/4=y/6`
`y/2=z/3=>y/6=z/9`
`-> x/4=y/6=z/9=>x/4=(2y)/12 =(3z)/27`
ADTC dãy tỉ số bằng nhau ta có :
`x/4=(2y)/12=(3z)/27=(x-2y+3z)/(4-12+27)=19/19=1`
`=>x/4=1=>x=1.4=4`
`=>y/6=1=>y=1.6=6`
`=>z/9=1=>z=1.9=9`
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x-\frac{1}{2}=y-\frac{2}{3}=z-\frac{3}{4}\)va \(x-2y+3z=14\)
\(\frac{\Rightarrow\left(x-1\right)}{2}=\frac{\left(-2y+4\right)}{-6}=\frac{\left(3z-9\right)}{12}\)
\(=\frac{\left(x-1-2y+4+3z-9\right)}{\left(2-6+12\right)}\)
\(\Rightarrow-\frac{16}{8}=-2\)
\(\frac{\Rightarrow\left(y-2\right)}{2}=-2\Leftrightarrow x-1=-4\Leftrightarrow x=-3\)
\(\Rightarrow\frac{\left(y-2\right)}{3}=-2\Leftrightarrow x-1=-4\Leftrightarrow x=-3\)
\(\Rightarrow\frac{\left(x-3\right)}{4}=-2\Leftrightarrow z-3=-8\Leftrightarrow z=-5\)
\(b)\)
Theo đề ra:
\(x:y:z=3:4:5\)
\(2x^2+2y^2-3z^2=-100\)
\(\Leftrightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)
\(\Leftrightarrow\frac{x^2}{9}=\frac{y^2}{16}=\frac{z^2}{25}\)
\(\Leftrightarrow\frac{2x^2}{18}=\frac{2y^2}{32}=\frac{3z^2}{75}\)
Áp dụng tính chất dãy tỷ số bằng nhau:
\(\frac{2x^2}{18}=\frac{2y^2}{32}=\frac{3z^2}{75}=\frac{2x^2+2y^2-3z^2}{18+32-75}=\frac{-100}{-25}=4\)
\(\Leftrightarrow\hept{\begin{cases}\frac{x}{3}=4\Leftrightarrow x=12\\\frac{y}{4}=4\Leftrightarrow y=16\\\frac{z}{5}=4\Leftrightarrow z=20\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\frac{x}{5}=\frac{y}{4}=\frac{z}{3}\)
Đặt \(\frac{x}{5}=\frac{y}{4}=\frac{z}{3}=k\Rightarrow\hept{\begin{cases}x=5k\\y=4k\\z=3k\end{cases}}\)
Khi đó P = \(\frac{x+2y-3z}{x-2y+3z}=\frac{5k+2.4k-3.3k}{5k-2.4k+3.3k}=\frac{5k+8k-9k}{5k-8k+9k}=\frac{4k}{6k}=\frac{2}{3}\)
Theo bài ra, ta có :
x:y:z=5:4:3 ⇒x/5=y/4=z/5⇒
Đặt x/5=y/4=z/3=kx5=y4=z3=k ⇒x=5k
y=4k
z=3k⇒x=5ky=4kz=3k
⇒P=x+2y−3z/x−2y+3z=5k+8k−9k/5k−8k+9k=4k/6k=23
Vậy P=23
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left[\left(-3,2\right)+\frac{2}{5}\right]\)
\(\Rightarrow\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left[-\frac{3}{2}+\frac{2}{5}\right]\)
\(\Rightarrow\left|x-\frac{1}{3}\right|+\frac{4}{5}=-\frac{11}{10}\)
\(\Rightarrow\left|x-\frac{1}{3}\right|=-\frac{11}{10}-\frac{4}{5}\)
\(\Rightarrow\left|x-\frac{1}{3}\right|=-\frac{19}{10}\)
\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{3}=\frac{19}{10}\\x-\frac{1}{3}=-\frac{19}{10}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{67}{30}\\x=-\frac{47}{30}\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(\frac{x}{5}=\frac{y}{4}=\frac{z}{3}=k\Rightarrow x=5k;y=4k;z=3k\)
=>\(P=\frac{x+2y-3z}{x-2y+3z}=\frac{5k+2.4k-3.3k}{5k-2.4k+3.3k}=\frac{5k+8k-9k}{5k-8k+9k}=\frac{4k}{6k}=\frac{2}{3}\)