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a, Ta có : \(\frac{1}{3}x=-\frac{1}{7}y\Leftrightarrow\frac{x}{3}=-\frac{y}{7}\)

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

\(\frac{x}{3}=-\frac{y}{7}=\frac{x-y}{3-\left(-7\right)}=-\frac{20}{10}=-10\)

\(x=-30;y=70\)

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

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

\(x=-15;y=-25\)

c, Đặt \(x=7k;y=13k\)

Ta có : \(xy=91\)Suy ra : \(7k.13k=91\Leftrightarrow91k=91\Leftrightarrow k=1\)

Thay k ta được : \(x=7;y=13\)

2/1.3+2/3.5+...+2/x(x+2)= 40/41

1-1/3+1/3-1/5+...+1/x-1/(x+2)=40/41

1-1/(x+2)=40/41

1/(x+2)=1-40/41=1/41

x+2=41

x=41-2=39

x = 1235

ta có: 1/3.5 +1/5.7 +...+1/x.(x+2)=20/41

=> 1/2(1/3-1/5+1/5-1/7+....+1/x-1/x+2)=20/41

=> 1/2(1/3-1/x+2)=20/41

=> 1/3-1/x+2=40/41

=> 1/x+2=1/3-40/41

=> 1/x+2=-79/123

Đề này có  gì đó sai sai bạn xem lại đề nhé

Ta có:

1/1.3 + 1/3.5 + 1/5.7 + ... + 1/x.(x+2) = 1/2.(2/1.3 + 2/3.5 + 2/5.7 + ... + 2/x.(x+2)

                                                          = 1/2.(1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/x+2

                                                          = 1/2.(1 - 1/x+2)

=> 1/2.(1 - 1/x+2) = 20/41

            1 - 1/x+ 2  = 20/41 : 1/2

            1 - 1/x+2   = 40/41

                  1/x+2  = 1/41

=>x + 2 = 41

=>x        = 41 - 2

=>x        = 39

Vậy x = 39

Ủng hộ nha

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x.\left(x+2\right)}=\frac{20}{41}\)

=> \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}=2.\frac{20}{41}\)

=> \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{40}{41}\)

=> \(1-\frac{1}{x+2}=\frac{40}{41}\)

=> \(\frac{1}{x+2}=1-\frac{40}{41}\)

=> \(\frac{1}{x+2}=\frac{1}{41}\)

=> \(x+2=41\)

=> \(x=41-2=39\)

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{20}{41}\)

\(\Leftrightarrow\)\(\frac{2}{1.3}+\frac{2}{3.4}+\frac{2}{5.7}+...+\frac{2}{x\left(x+2\right)}=\frac{40}{41}\)

\(\Leftrightarrow\)\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{40}{41}\)

\(\Leftrightarrow\)\(1-\frac{1}{x+2}=\frac{40}{41}\)

\(\Leftrightarrow\)\(\frac{1}{x+2}=1-\frac{40}{41}\)

\(\Leftrightarrow\)\(\frac{1}{x+2}=\frac{1}{41}\)

\(\Leftrightarrow\)\(x+2=41\)

\(\Leftrightarrow\)\(x=41-2\)

\(\Leftrightarrow\)\(x=39\)

Đề sai rồi bạn ơi

Phải là 1/x.(x+2)

Gọi tổng trên là A

1/2A= 2/1.3+1/3.5+...+1/x.(x+2)

1/2A= 1-1/x.(x+2)

A=\(\frac{1-\frac{1}{x.\left(x+2\right)}}{2}\)

cảm ơn

Ta có: \(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{x\left(x+2\right)}=\dfrac{20}{41}\)

\(\Leftrightarrow\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{40}{41}\)

\(\Leftrightarrow1-\dfrac{2}{x+2}=\dfrac{40}{41}\)

\(\Leftrightarrow\dfrac{2}{x+2}=\dfrac{1}{41}\)

Suy ra: x+2=82

hay x=80

x * 6,5  = 20 - 3,5 

x * 6,5 = 16 ,5 

x = 16 ,5 : 6,5 

x = 2 ,538461...

k nha

X = 2 nhé

6.5 + 3.5 = 10

20 : 10 = 2

X x 6,5 + 3,5 = 20

X x 6,5 = 16,5

X = 16,5 : 6,5

X = 2,5384....