\(\frac{x-1}{2}=\frac{y+3}{3}=\frac{z-5}{6}\)\(\Rightarrow\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)

áp dụng tính chất của dãy tỉ số bằng nhau ta có

\(\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}=\frac{5z-30-3x+3-4y-12}{30-16-6}=\frac{50-34}{8}=\frac{16}{8}=2\)

Cái sai của bạn là sao không ghép với cái phân số ban đầu=> hệ số nhỏ đỡ mệt hơn không

x-1=2.2=> x=5 

y+3=4.2=> y=5

z-5=6.2=>z=17

Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\) 

\(\Rightarrow\) \(\frac{z-5}{6}=\frac{x-1}{2}=\frac{y+3}{4}\) 

\(\Rightarrow\frac{5z-25}{30}=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{\left(5z-3x-4y\right)-25+3-12}{30-6-16}=\frac{50-34}{8}=\frac{16}{8}=2\)

\(\Rightarrow\)x = 5

     y = 5

     z = 17

x-1/2=y+3/4=z-5/6=k suy ra x-1=2k;y+3=4k;z-5=6k va x=2k+1;y=4k-3;z=6k+5

5(6k+5)-3(2k+1)-4(4k-3)=25+30k-3+6k-16k-12=(25-3-12)+(30k+6k-16k)

=10+20k=50  suy ra 20k=50-10=40 suy ra k=40:20=2

x=2.2+1=5

y=2.4-3=5

z=2.6+5=17

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

=> \(\frac{3\left(x-1\right)}{6}=\frac{4\left(y+3\right)}{16}=\frac{5\left(z-5\right)}{30}\)

=> \(\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)

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

\(\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}=\frac{5z-25-3x+3-4y-12}{30-6-16}=\frac{50-34}{8}=\frac{16}{8}=2\)

=> 3x - 3 = 12 => 3x = 15 => x = 5

    4y + 12 = 32 => 4y = 20 => y = 5

    5z - 25 = 60 => 5z = 85 => z = 17

Vậy x = 5 , y = 5 , z = 17

1, ta co \(\frac{x}{5}=\frac{y}{6}=\frac{x}{20}=\frac{y}{24}\)

\(\frac{y}{8}=\frac{z}{7}=\frac{y}{24}=\frac{z}{21}\)

=>\(\frac{x}{20}=\frac{y}{24}=\frac{z}{21}=\frac{x+y-z}{20+24-21}=\frac{69}{23}=3\)

=>\(x=3\cdot20=60\)

    \(y=3\cdot24=72\)

    \(z=3\cdot21=63\)

3. ta co \(\frac{x}{15}=\frac{y}{7}=\frac{z}{3}=\frac{t}{1}=\frac{x+y-z+t}{15-7+3-1}=\frac{10}{10}=1\)

=> \(x=1\cdot15=15\)

     \(y=1\cdot7=7\)

     \(z=1\cdot3=3\)

     \(t=1\cdot1=1\)

Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)

\(=\frac{3\left(x-1\right)}{6}=\frac{4\left(y+3\right)}{16}=\frac{5\left(z-5\right)}{30}\)

\(=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)\(=\frac{5z-25-3x+3-4y-12}{6-16-30}\)\(=\frac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{-40}\)\(=\frac{50-34}{-40}=\frac{16}{-40}=\frac{2}{-5}\)

+) \(\frac{x-1}{2}=\frac{-2}{5}\Rightarrow5\left(x-1\right)=-4\Rightarrow x-1=\frac{-4}{5}\)\(\Rightarrow x=\frac{-4}{5}+1=\frac{1}{5}\)

+)\(\frac{y+3}{4}=\frac{-2}{5}\Rightarrow5\left(y+3\right)=-8\Rightarrow y+3=\frac{-8}{5}\)\(\Rightarrow y=\frac{-8}{5}-3=\frac{-23}{5}\)

+)\(\frac{z-5}{6}=\frac{-2}{5}\Rightarrow5\left(z-5\right)=-12\Rightarrow z-5=\frac{-12}{5}\)\(\Rightarrow z=\frac{-12}{5}+5=\frac{13}{5}\)

Vậy...

lúc nào bạn cần?

Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\Leftrightarrow\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4y-20}{24}\)

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

\(\frac{-3x+3}{-6}=\frac{4y+12}{16}=\frac{5z-25}{30}=\frac{-3x+3-4y-12+5z-25}{10-12+30}=\frac{\left(5z-3x-4y\right)+\left(3-12-25\right)}{28}=\frac{50-34}{28}=\frac{4}{7}\)

tới đay tự tính

\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\Rightarrow\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)

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

\(\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}=\frac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\)\(=\frac{5z-25-3x+3-4y-12}{30-6-16}=\frac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{8}=\frac{50-34}{8}=\frac{16}{8}=2\)

Khi đó:\(\frac{3x-3}{6}=2\Rightarrow\frac{x-1}{2}=2\Rightarrow x=5;\frac{4y+12}{16}=2\Rightarrow\frac{y+3}{4}=2\Rightarrow y=5\)

\(\frac{5z-25}{30}=2\Rightarrow\frac{z-5}{6}=2\Rightarrow z=17\)

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

ta có:

\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}=>\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)

\(=\frac{5z-25-\left(3x-3\right)-\left(4y+12\right)}{30-16-6}\)\(=\frac{5z-25-3x+3-4y-12}{8}=\frac{5z-3x-4y-34}{8}\)

\(=\frac{50-34}{8}=\frac{16}{8}=2\)

Vậy x=5;y=5;z=17

Theo đầu bài ta có:
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
\(\Rightarrow\frac{3\left(x-1\right)}{3\cdot2}=\frac{4\left(y+3\right)}{4\cdot4}=\frac{5\left(z-5\right)}{5\cdot6}\)
\(\Rightarrow\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{5z-25}{30}\)
\(=\frac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\)
\(=\frac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{8}\)
\(=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\Rightarrow\hept{\begin{cases}x=2\cdot2+1=5\\y=2\cdot4-3=5\\z=2\cdot6+5=17\end{cases}}\)

k tớ đi rồi tớ làm