\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\Rightarrow\frac{2x-2}{4}=\frac{3y-6}{6}=\frac{z-3}{4}\)

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

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

\(=\frac{\left(2x+3y-z\right)+\left(-2+6+3\right)}{6}=\frac{50+\left(-5\right)}{6}=\frac{45}{6}=7,5\)

\(\frac{x-1}{2}=7,5\Rightarrow x-1=15\Rightarrow x=16\)

\(\frac{y-2}{3}=7,5\Rightarrow y-2=24,5\Rightarrow y=20,5\)

\(\frac{z-3}{4}=7,5\Rightarrow z-3=30\Rightarrow z=33\)

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

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

Từ (1) và (2) => 2x+3y-z=\(2x+3\left(\frac{3\left(x-1\right)+4}{2}\right)-\frac{4\left(x-1\right)+6}{2}=50\)

\(\Rightarrow\frac{4x}{2}+\frac{9\left(x-1\right)+12}{2}-\frac{4\left(x-1\right)+6}{2}=50\)

\(\Rightarrow\frac{4x+9x-9+12-4x+4-6}{2}=50\)

\(\Rightarrow9x+1=100\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=11\)

Vì \(y=\frac{3\left(x-1\right)+4}{2}=\frac{3\left(11-1\right)+4}{2}=\frac{34}{2}=17\Leftrightarrow y=17\)

Vì \(z=\frac{4\left(x-1\right)+6}{2}=\frac{4\left(11-1\right)+6}{2}+\frac{46}{2}=23\Leftrightarrow z=23\)

Vậy   x=11

         y=17

         z=23

\(\Rightarrow\frac{2\left(x-1\right)}{2.2}=\frac{3\left(y-2\right)}{3.3}=\frac{z-3}{4}\) 

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

Áp dụng t/c dãy tỉ số = nhau

\(\Rightarrow\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{50-2-6+3}{9}=\frac{45}{9}=5\) 

\(\Rightarrow\hept{\begin{cases}\frac{x-1}{2}=5\Rightarrow x-1=10\Rightarrow x=11\\\frac{y-2}{3}=5\Rightarrow y-2=15\Rightarrow y=17\\\frac{z-3}{4}=5\Rightarrow z-3=20\Rightarrow z=23\end{cases}}\)

Ta có: \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)=> \(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{-z-3}{4}\)

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

\(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{-z-3}{4}=\frac{2x-2+3y-6-z+3}{4+9-4}\)= \(\frac{50-2-6+3}{9}=\frac{45}{9}=5\).

=> \(\hept{\begin{cases}\frac{x-1}{2}=5\\\frac{y-2}{3}=5\\\frac{z-3}{4}=5\end{cases}}\)=> \(\hept{\begin{cases}x-1=10\\y-2=15\\z-3=20\end{cases}}\)=> \(\hept{\begin{cases}x=11\\y=17\\z=23\end{cases}}\).

Ta có: 2x + 3y + 5z - 119 = 0

=>  2x + 3y + 5z = 119

 \(\frac{x+2}{3}=\frac{y+3}{5}=\frac{z-4}{7}\Leftrightarrow\frac{2x+4}{6}=\frac{3y+9}{15}=\frac{5z-20}{35}\)

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\frac{2x+4}{6}=\frac{3y+9}{15}=\frac{5z-20}{35}=\frac{2x+4+3y+9+5z-20}{6+15+35}=\frac{119+4+9-20}{56}=\frac{112}{56}=2\)

\(\Rightarrow\hept{\begin{cases}\frac{x+2}{3}=2\\\frac{y+3}{5}=2\\\frac{z-4}{7}=2\end{cases}\Rightarrow}\hept{\begin{cases}x+2=6\\y+3=10\\z-4=14\end{cases}}\Rightarrow\hept{\begin{cases}x=4\\y=7\\z=18\end{cases}}\)

Vậy...

https://olm.vn/hoi-dap/detail/233628753470.html

Đặt x=2z;y=3z

=> B=(5x2z+3x3z)/(6x2z-7x3z)

=(19z)/(-9z)

=-19/9

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)+3\left(y-2\right)-\left(z-3\right)}{4+9-4}\)

                                                   \(=\frac{2x-2+3y-6-x+3}{9}=\frac{50-5}{9}=5\)

Suy ra: \(x-1=10\Rightarrow x=11\)

           \(y-2=15\Rightarrow y=17\)

             \(z-3=20\Rightarrow z=23\)

- Cám ơn bạn nhìu nha

Áp dụng tc dãy TSBN có:

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}=\frac{50-5}{9}=5\)

Ta có:2x+y=z−38⇒2x+y−z=−382x+y=z−38⇒2x+y−z=−38

Vì 3x=4y=5x−3x−4y3x=4y=5x−3x−4y nên 3x=5z−3x−3x3x=5z−3x−3x

⇒3x−5z−6x⇒3x−5z−6x

⇒9x=5z⇒9x=5z

⇒x5=z9⇒x20=z36⇒x5=z9⇒x20=z36(1)

Vì 3x=4y⇒x4=y3⇒x20=z153x=4y⇒x4=y3⇒x20=z15 (2)

Từ (1) và (2)⇒x20=y15=z36⇒x20=y15=z36

Áp dụng tính chất dãy tỉ số bằng nhau:

x20=y15=z36=2x+y−z2.20+15−36=−3819=−2x20=y15=z36=2x+y−z2.20+15−36=−3819=−2

x20=−2⇒x=20.(−2)=−40x20=−2⇒x=20.(−2)=−40

y15=−2⇒y=15.(−2)=−30y15=−2⇒y=15.(−2)=−30

z36=−2⇒z=36.(−2)=−72z36=−2⇒z=36.(−2)=−72

Vậy x=−40;y=−30;z=−72

dễ mà 2/5 =6/7 em ak =)

cảm ơn nha

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