\(\dfrac{x+y}{13}\) = \(\dfrac{x-y}{3}\) = \(\dfrac{xy}{200}\)

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

\(\dfrac{xy}{200}\) = \(\dfrac{x+y}{3}\) = \(\dfrac{x+y+x-y}{13+3}\) = \(\dfrac{2x}{16}\)

      \(\dfrac{xy}{200}\) = \(\dfrac{2x}{16}\)

     \(\dfrac{xy}{200}-\dfrac{2x}{16}\) = 0

     \(x\) x (\(\dfrac{y}{200}\) - \(\dfrac{2}{16}\)) = 0

      \(x\) = 0 hoặc \(\dfrac{y}{200}\) - \(\dfrac{2}{16}\) = 0 ⇒ y = \(\dfrac{2}{16}\) x 200

      y = 25 

Nếu \(x\) = 0 ⇒ \(\dfrac{0+y}{13}\) = 0 ⇒ y = 0

Nếu y = 25 thì \(\dfrac{x+25}{13}\) = \(\dfrac{25x}{200}\) = \(\dfrac{x}{8}\)

                       8\(x\) + 200 = 13\(x\)

                      13\(x\) - 8\(x\) = 200

                            5\(x\)    = 200

                              \(x\)   = 200 : 5

                             \(x\)   = 40

Vậy (\(x;y\)) = (0; 0); (40; 25)

\(\frac{x+y}{13}=\frac{x-y}{3}=\frac{xy}{200}\)

\(\Rightarrow3\left(x+y\right)=13\left(x-y\right)\)

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

\(\frac{x-y}{3}=\frac{xy}{200}\Rightarrow200\left(x-y\right)=3xy\)

\(\Rightarrow200\left(x-\frac{5x}{8}\right)=\frac{3x.5x}{8}\Rightarrow x^2-40x\Rightarrow x\left(x-40\right)=0\)

\(\Rightarrow x=\left[\begin{array}{nghiempt}0\\40\end{array}\right.\)\(\Leftrightarrow y=\left[\begin{array}{nghiempt}0\\25\end{array}\right.\)

Áp dụng tính chất dãy tỉ số bằng nhau , ta có 
  \(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y+x+y}{13+3}=\frac{2x}{16}=\frac{x}{8}\)
\(\frac{xy}{200}=\frac{x}{8}=\frac{25x}{200} \)
\(\Rightarrow xy=25x\Rightarrow y=25\)
Ta có : \(\frac{x+y}{13}=\frac{x-y}{3}\)
hay \(\frac{x+25}{13}=\frac{x-25}{3}\)
\(\Rightarrow3x+75=13x-325\)
 \(-10x=-400\)
        \(x=-400:-10=40\)
Vậy x = 40
      y = 25
100% đúng đấy bạn
        

 

+x =0 => y =0

+\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x+y-x+y}{13-3}=\frac{2y}{10}=\frac{y}{5}=\frac{xy}{5x}=\frac{xy}{200}\)

=> 5x =200 => x =40

\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{2x}{16}=\frac{x}{8}=\frac{y}{5}\)

=> y =5.40/8 = 25

Vậy (x;y) = (0;0); (40;25)

Ta có: \(\frac{x-y}{3}=\frac{x+y}{13}\)

=> (x - y).13 = 3.(x + y)

=> 13x - 13y = 3x + 3y

=> 13x - 3x = 3y + 13y

=> 10x = 16y

=> \(x=\frac{16}{10}y=\frac{8}{5}y\)

Thay \(x=\frac{8}{5}y\) vào đề bài ta có: \(\frac{\frac{8}{5}y-y}{3}=\frac{\frac{8}{5}y+y}{13}=\frac{\frac{8}{5}y.y}{200}\)

\(\Rightarrow\frac{\frac{3}{5}y}{3}=\frac{\frac{13}{5}y}{13}=\frac{\frac{8}{5}y^2}{200}\)

\(\Rightarrow\frac{3}{5}y.\frac{1}{3}=\frac{13}{5}y.\frac{1}{13}=\frac{8}{5}y^2.\frac{1}{200}\)

\(\Rightarrow\frac{1}{5}y=\frac{1}{125}.y^2\)

\(\Rightarrow\frac{1}{5}y-\frac{1}{125}.y^2=0\)

\(\Rightarrow\frac{1}{5}y.\left(1-\frac{1}{25}y\right)=0\)

\(\Rightarrow\left[\begin{array}{nghiempt}y=0\\1-\frac{1}{25}y=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}y=0\\\frac{1}{25}y=1\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}y=0\\y=25\end{array}\right.\)

+ Với y = 0 thì \(x=\frac{8}{5}.0=0\)

+ Với y = 25 thì \(x=\frac{8}{5}.25=40\)

Vậy \(\begin{cases}x=0\\y=0\end{cases}\); \(\begin{cases}x=40\\y=25\end{cases}\)

\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y+x+y}{3+13}=\frac{2x}{16}=\frac{x}{8}=\frac{25x}{200}=\frac{xy}{200}\)

Vì 25x = xy nên y = 25

\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y-x-y}{3-13}=\frac{-2y}{-10}=\frac{y}{5}\)

=> \(\frac{y}{5}=\frac{x}{8}\Rightarrow8y=5x\Rightarrow\frac{x}{y}=\frac{8}{5}\)

=> x = 40 

Vậy...

ngu thees

Nguyễn Hải Đăng chắc bn giỏi nói ng ta ngu :(( 

\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y-x-y}{3-13}=\frac{-2y}{-10}=\frac{y}{5}\)

\(\Rightarrow\frac{y}{5}=\frac{xy}{200}\Rightarrow200y=5xy\Rightarrow\frac{200y}{5y}=x\Rightarrow x=40\)

\(\frac{x-y}{3}=\frac{y}{5}=\frac{40-y}{3}=\frac{y}{5}\Rightarrow5.\left(40-y\right)=3y\Rightarrow200-5y=3y\)

\(\Rightarrow200=8y\Rightarrow y=25\)

Vậy x=40, y=25

Ta có :

\(\frac{x-y}{3}=\frac{x+y}{13}=\frac{x-y+x+y}{3+13}=\frac{2x}{16}=\frac{25x}{200}=\frac{xy}{200}\)

\(\Rightarrow25x=xy\Rightarrow y=25\)

\(\Rightarrow\frac{x-25}{3}=\frac{x+25}{13}\)

\(\Leftrightarrow13x-325=3x+75\)

\(\Leftrightarrow10x=400\Rightarrow x=40\)

Vậy \(x=40;y=25\)

mình thấy câu này cx không qua khó bạn chỉ cần động não thôi