Ta có:\(\frac{2x-y}{x+y}=\frac{2}{3}\)

\(\Rightarrow3\left(2x-y\right)=2\left(x+y\right)\)

\(\Rightarrow6x-3y=2x+2y\)

\(\Rightarrow4x=5y\)

\(\Rightarrow\frac{x}{y}=\frac{5}{4}\)

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

\(\Rightarrow2x-y=4y-2x\Rightarrow4x=5y\Rightarrow\frac{x}{y}=\frac{5}{4}\)

Áp dụng công thức lớp 7 ; \(\frac{a}{b}\)= \(\frac{c}{d}\) thì \(\frac{a}{c}\)= \(\frac{b}{d}\)

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

=> .....................................x/y = 5/4

Ta có: \(\frac{2x-y}{x+y}\)=\(\frac{2}{3}\)

=> (2x - y).3 = (x+y) .2

6x - 3y = 2x + 2y

6x - 2x = 3y + 2y

4x = 5y

=> \(\frac{x}{5}\)=\(\frac{y}{4}\)

Vậy tỉ số \(\frac{x}{y}\)=\(\frac{5}{4}\)

\(\frac{2x-y}{x+y}=\frac{2}{3}\)

\(\Rightarrow3\left(2x-y\right)=2\left(x+y\right)\)

\(\Rightarrow6x-3y=2x+2y\)

\(\Rightarrow6x-2x=2y+3y\)

\(\Rightarrow4x=5y\)

\(\Rightarrow\frac{x}{y}=\frac{5}{4}\)

Vậy \(\frac{x}{y}=\frac{5}{4}\)

Theo bài ra ta có: \(\frac{2x-y}{x+y}=\frac{2}{3}\)

=> 3(2x-y)=2(x+y)

=> 6x-3y=2x+2y

=> 6x-2x=2y+3y

=> 4x=5y

=> \(\frac{x}{y}=\frac{5}{4}\)

Vậy \(\frac{x}{y}=\frac{5}{4}\)

Ta có : \(\frac{2x-y}{x+y}=\frac{2}{3}\Leftrightarrow3\left(2x-y\right)=2\left(x+y\right)\Leftrightarrow6x-3y=2x+2y\Leftrightarrow4x=5y\Leftrightarrow\frac{x}{y}=\frac{5}{4}\)

Vì \(\frac{2x-y}{x+y}=\frac{2}{3}=>\left(2x-y\right).3=\left(x+y\right).2=>6x-3y=2x+2y\)

\(=>6x-2x=2y-\left(-3y\right)=>6x-2x=2y+3y=>4x=5y=>\frac{x}{y}=\frac{5}{4}\)

Vậy tỉ số x/y=5/4

a) \(\frac{1}{2}-|\frac{5}{4}-2x|=\frac{1}{3}\Leftrightarrow|\frac{5}{4}-2x|=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{5}{4}-2x=\frac{1}{6}\\\frac{5}{4}-2x=-\frac{1}{6}\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=\frac{5}{4}-\frac{1}{6}=\frac{13}{12}\\2x=\frac{5}{4}+\frac{1}{6}=\frac{17}{12}\end{cases}}}\)

Tự làm nốt và kết luận 

b) \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}+\frac{1}{14}\right)=0\)

Vì \(\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}+\frac{1}{14}\right)\ne0\forall x\Rightarrow x+1=0\Leftrightarrow x=-1\)

Vậy ....

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

\(\Leftrightarrow\frac{x}{10}=\frac{y}{9}=\frac{z}{12}\). Mà \(x-y+z=78\). Áp dụng t/c dãy tỉ số bằng nhau 

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

\(\Rightarrow x=6.10=60;y=6.9=54;z=6.12=72\)

Vậy..........

\(\frac{2x-y}{x+y}=\frac{2}{3}\)

\(\Rightarrow3\left(2x-y\right)=2\left(x+y\right)\)

\(\Rightarrow6x-3y=2x+2y\)

\(\Rightarrow6x-2x=3y+2y\)

\(\Rightarrow4x=5y\)

\(\Rightarrow\frac{x}{y}=\frac{5}{4}\)

\(\Rightarrow\frac{2x+2y-3y}{x+y}=\frac{2}{3}\)

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

\(\Rightarrow2-\frac{3y}{x+y}=\frac{2}{3}\)

\(\Rightarrow\frac{3y}{x+y}=2-\frac{2}{3}\)

\(\Rightarrow\frac{3y}{x+y}=\frac{4}{3}\)

\(\Rightarrow3y.3=\left(x+y\right).4\)

\(\Rightarrow9y=4x+4y\)

\(\Rightarrow5y=4x\)

\(\Rightarrow\frac{x}{y}=\frac{5}{4}\)

post từng câu một thôi bn nhìn mệt quá

ta có 

​\(\frac{x}{3}\)=\(\frac{y}{2}\)=> \(\frac{x}{9}\)=\(\frac{y}{6}\)

\(\frac{y}{3}\)=\(\frac{z}{5}\)=>\(\frac{y}{6}\)=\(\frac{z}{10}\)

=>\(\frac{x}{9}\)=\(\frac{y}{6}\)=\(\frac{z}{10}\)

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

    \(\frac{x}{9}\)=\(\frac{y}{6}\)=\(\frac{z}{10}\)=> \(\frac{2x}{18}\)=\(\frac{y}{6}\)=\(\frac{3z}{30}\)=\(\frac{2x-y+3z}{18-6+30}\)=\(\frac{42}{42}\)=1

Ta lại có:

     \(\frac{2x}{18}\)= 1=> 2x=18=>x=9

       \(\frac{y}{6}\)= 1 =>y=6

      \(\frac{3z}{30}\)= 1=>3z=30=>z=10

 Vậy x=9 ; y=6 và z=10

a/ \(M=\left(x^2+\frac{1}{y^2}\right)\left(y^2+\frac{1}{x^2}\right)=x^2y^2+\frac{1}{x^2y^2}+2=\left(xy-\frac{1}{xy}\right)^2+4\ge4\)

Suy ra Min M = 4 . Dấu "=" xảy ra khi x=y=1/2

b/ Đề đúng phải là \(\frac{1}{3x+3y+2z}+\frac{1}{3x+2y+3z}+\frac{1}{2x+3y+3z}\ge\frac{3}{2}\)

Ta có \(6=\frac{1}{x+y}+\frac{1}{y+z}+\frac{1}{z+x}\ge\frac{9}{2\left(x+y+z\right)}\Rightarrow x+y+z\ge\frac{3}{4}\)

Lại có \(\frac{1}{3x+3y+2z}+\frac{1}{3x+2y+3z}+\frac{1}{2x+3y+3z}\ge\frac{9}{8\left(x+y+z\right)}\ge\frac{9}{8.\frac{3}{4}}=\frac{3}{2}\)