\(\dfrac{3x}{2}=\dfrac{4y}{3}=\dfrac{6z}{5}\Rightarrow\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{4}}=\dfrac{z}{\dfrac{5}{6}}\)

Áp dụng t/c dtsbn:

\(\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{4}}=\dfrac{z}{\dfrac{5}{6}}=\dfrac{x+y-z}{\dfrac{2}{3}+\dfrac{3}{4}-\dfrac{5}{6}}=\dfrac{-21}{\dfrac{7}{12}}=-36\\ \Rightarrow\left\{{}\begin{matrix}x=-36\cdot\dfrac{2}{3}=-24\\y=-36\cdot\dfrac{3}{4}=-27\\z=-36\cdot\dfrac{5}{6}=-30\end{matrix}\right.\)

\(\frac{2}{3x}=\frac{3}{4y}=\frac{5}{6z}\Rightarrow\frac{2}{30.3x}=\frac{3}{30.4y}=\frac{5}{30.6z}\Leftrightarrow\frac{1}{45x}=\frac{1}{40y}=\frac{1}{36z}\Rightarrow45x=40y=36z\)

\(\Rightarrow x=\frac{9}{8}y;x=\frac{5}{4}z\Rightarrow x^2+y^2+z^2=x^2+\frac{64}{81}x^2+\frac{16}{25}x^2\)

\(=x^2\left(1+\frac{2896}{2025}\right)=724\text{ :)) đến đây thôi :))}\)

Ko bạn ơi , mik ko viết rõ nên bạn lầm á . Phải là \(\frac{2}{3}x=\frac{3}{4}y=\frac{5}{6}z\)và x²+ y²+ z²=724

1)

a) 3x = 4y \(\Rightarrow\frac{x}{4}=\frac{y}{3}\)\(\Rightarrow\frac{x}{8}=\frac{y}{6}\)( 1 )

5y = 6z \(\Rightarrow\frac{y}{6}=\frac{z}{5}\)( 2 )

Từ ( 1 ) và ( 2 ) \(\Rightarrow\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=\frac{x+y+z}{8+6+5}=\frac{1}{19}\)

\(\Rightarrow x=\frac{8}{19};y=\frac{6}{19};z=\frac{5}{19}\)

b) \(\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-3}{5}\Rightarrow\frac{3x-3}{9}=\frac{4y-8}{16}=\frac{5z-15}{25}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có :

\(\frac{3x-3}{9}=\frac{4y-8}{16}=\frac{5z-15}{25}=\frac{\left(3x-3\right)+\left(4y-8\right)+\left(5z-15\right)}{9+16+25}=\frac{-25}{50}=\frac{-1}{2}\)

\(\Rightarrow x=\frac{-1}{2};y=0;z=\frac{1}{2}\)

\(\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1,6+\frac{3}{5}\right|\)

\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1,6+0,6\right|\)

\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=\left|-1\right|\)

\(\Rightarrow\left|x-\frac{1}{2}\right|+\frac{3}{4}=1\)

\(\Rightarrow\left|x-\frac{1}{2}\right|=1-\frac{3}{4}\)

\(\Rightarrow\left|x-\frac{1}{2}\right|=\frac{1}{4}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{1}{4}\\x-\frac{1}{2}=-\frac{1}{4}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=\frac{1}{4}\end{cases}}}\)

Vậy ...

\(1)\) Ta có : 

\(3x=4y\)\(\Leftrightarrow\)\(\frac{x}{4}=\frac{y}{3}\)\(\Leftrightarrow\)\(\frac{x}{8}=\frac{y}{6}\)

\(5y=6z\)\(\Leftrightarrow\)\(\frac{y}{6}=\frac{z}{5}\)

\(\Rightarrow\)\(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}\)

Đặt \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=k\)\(\Rightarrow\)\(\hept{\begin{cases}x=8k\\y=6k\\z=5k\end{cases}}\) \(\left(1\right)\)

Thay \(\left(1\right)\) vào \(xyz=30\) ta được : 

\(8k.6k.5k=30\)

\(\Leftrightarrow\)\(240k^3=30\)

\(\Leftrightarrow\)\(k^3=\frac{30}{240}\)

\(\Leftrightarrow\)\(k^3=\frac{1}{8}\)

\(\Leftrightarrow\)\(k^3=\left(\frac{1}{2}\right)^3\)

\(\Leftrightarrow\)\(k=\frac{1}{2}\)

Suy ra : 

\(x=8k=8.\frac{1}{2}=\frac{8}{2}=4\)

\(y=6k=6.\frac{1}{2}=\frac{6}{2}=3\)

\(z=5k=5.\frac{1}{2}=\frac{5}{2}\)

Vậy \(x=4\)\(;\)\(y=3\) và \(z=\frac{5}{2}\)

Chúc bạn học tốt ~ 

Ta có : 

\(3x=4y\Rightarrow\frac{x}{4}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{6}\left(1\right)\)

\(5y=6z\Rightarrow\frac{y}{6}=\frac{z}{5}\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\)

\(\Rightarrow\frac{x}{8}=\frac{y}{6}=\frac{z}{5}\)

Đặt \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=k\left(k\ne0\right)\)

\(\Rightarrow x=8k;y=6k;z=5k\)

\(\Rightarrow xyz=8k.6k.5k\)

\(\Rightarrow xyz=240k^3\)

Do \(xyz=30\)

\(\Rightarrow240k^3=30\)

\(\Rightarrow k^3=\frac{1}{8}\)

\(\Rightarrow k=\frac{1}{2}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{1}{2}.8=4\\y=\frac{1}{2}.6=3\\z=\frac{1}{2}.5=2,5\end{cases}}\)

Vậy \(x=4;y=3;z=2,5\)

a ) x/2=y/5 suy ra x/4=y/10

x/4=z/3 suy ra x/4=2z/3

suy ra x/4=y/10=2z/3=x+y-2z/4+10-6=8/8=1

x/4=1 suy ra x=1*4=4

y/10=1 suy ra y=10*1=10

z/3=1 suy ra z=3*1=3

1) \(\frac{x}{2}=\frac{y}{3}=\frac{z}{7}=\frac{2x-4y+3z}{2.2-4.3+3.7}=\frac{-39}{13}=-3\)

\(\Leftrightarrow\hept{\begin{cases}x=-3.2=-6\\y=-3.3=-9\\z=-3.7=-21\end{cases}}\)

2) \(9x=10y\Leftrightarrow\frac{x}{10}=\frac{y}{9},4y=3z\Leftrightarrow\frac{y}{9}=\frac{z}{12}\)

suy ra \(\frac{x}{10}=\frac{y}{9}=\frac{z}{12}=\frac{x-y+z}{10-9+12}=\frac{78}{13}=6\)

\(\Leftrightarrow\hept{\begin{cases}x=6.10=60\\y=6.9=54\\z=6.12=72\end{cases}}\)

3) \(3x=4y=6z\Leftrightarrow\frac{x}{4}=\frac{y}{3}=\frac{z}{2}=\frac{x-y+z}{4-3+2}=\frac{-9}{3}=-3\)

\(\Leftrightarrow\hept{\begin{cases}x=-3.4=-12\\y=-3.3=-9\\z=-3.2=-6\end{cases}}\)

\(a,4x=5y\:\Rightarrow\frac{x}{5}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{12}\)

\(4y=6z\Rightarrow\frac{y}{6}=\frac{z}{4}\Rightarrow\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{x}{15}=\frac{2y}{24}=\frac{3z}{24}\)

\(\Rightarrow\frac{x-2y+3z}{15-24+24}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{5}{15}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{1}{3}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\cdot15=5\\y=\frac{1}{3}\cdot12=4\\z=\frac{1}{3}\cdot8=\frac{8}{3}\end{cases}}\)

mọi người giúp mk câu b, c, d còn lại nha

Theo đề bài ta có : x−12=y+34=z−56x−12=y+34=z−56 và 5z−3x−4y=505z−3x−4y=50

\Leftrightarrow 3(x−1)6=4(y+3)16=5(z−5)303(x−1)6=4(y+3)16=5(z−5)30 và 5z−3x−4y=505z−3x−4y=50

\Leftrightarrow 3x−36=4y+1216=5z−25303x−36=4y+1216=5z−2530 và 5z−3x−4y=505z−3x−4y=50

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

3x−36=4y+1216=5z−2530=(5z−25)−(3x−3)−(4y+12)30−6−16=5z−3x−4y−25+3−128=168=23x−36=4y+1216=5z−2530=(5z−25)−(3x−3)−(4y+12)30−6−16=5z−3x−4y−25+3−128=168=2

\Rightarrow x−12=2x−12=2 \Rightarrow x−1=4x−1=4 \Leftrightarrow x=5x=5

\Rightarrow y+34=2y+34=2 \Rightarrow y+3=8y+3=8 \Leftrightarrow y=5y=5

\Rightarrow z−56=2z−56=2 \Rightarrow z−5=12z−5=12 \Leftrightarrow z=17z=17

tk nha bạn