1 + 2 + 3 + ... + x = 45.

( x + 1 ) . x : 2 = 45.

( x + 1 ) . x = 90.

( x + 1 ) . x = 10 . 9.

Vậy x = 9.

Sửa đề:\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{2}{72}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(2\left(\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2}{9}\)

\(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2}{9}:2\)

\(\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{2}{9}.\dfrac{1}{2}\)

\(\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{2}{18}\)

\(\dfrac{1}{x+1}=\dfrac{1}{6}-\dfrac{1}{9}\)

\(\dfrac{1}{x+1}=\dfrac{3}{18}-\dfrac{2}{18}\)

\(\dfrac{1}{x+1}=\dfrac{1}{18}\)

\(x+1=18\)

\(x=18-1\)

\(x=17\)

`#H`

k)

<=> \(\left(\dfrac{7}{2}-2x\right):\dfrac{10}{3}=\dfrac{22}{3}\)

<=> \(\dfrac{7}{2}-2x=\dfrac{22}{3}\times\dfrac{10}{3}=\dfrac{220}{9}\)

=> \(2x=\dfrac{7}{2}-\dfrac{220}{9}=\dfrac{-377}{18}\)

=> \(x=\dfrac{-377}{18}:2=\dfrac{-377}{36}\)

 j , \(720:\left[41-\left(2x+5\right)\right]=40\)

\(41-\left(2x+5\right)=720:40\)

\(41-\left(2x+5\right)=18\)

\(2x+5=41-18\)

\(2x+5=23\)

2x =28

=> x=9

k,

\(\left(3\dfrac{1}{2}-2x\right):3\dfrac{1}{3}=7\dfrac{1}{3}\)

\(\left(\dfrac{7}{2}-2x\right):\dfrac{10}{3}=\dfrac{22}{3}\)

\(\dfrac{7}{2}-2x=\dfrac{22}{3}\cdot\dfrac{10}{3}\)

\(\dfrac{7}{2}-2x=\dfrac{220}{9}\)

\(2x=\dfrac{7}{2}-\dfrac{220}{9}\)

\(2x=-\dfrac{377}{18}\)

x=\(-\dfrac{377}{36}\)

Mình nghĩ câu cuối đề sai phải là 2/x(x+1) chứ nhỉ ?

`2/3<(1/6+2/15+3/40+4/96):5 xx x<5/6`

`2/3<(1/6+2/15+3/40+1/24):5 xx x<5/6`

`2/3<(20/120+48/120+9/120+5/120):5 xx x<5/6`

`2/3<82/120:5xx x<5/6`

`2/3<41/60:5 xx x<5/6`

`2/3<41/60xx1/5 xx x <5/6`

`2/3<41/300 xx x<5/6`

`2/3<(41x)/300<5/6`

`200/300<(41x)/300<25/300`

`200<41x<250`

`41x in {205;246}`

`x in {5;6}`

1/12

Ta có `:`

`x/2 = y/3 -> x/10 = y/15(1)`

`y/5 = z/7 -> y/15 = z/21(2)`

Từ `(1)(2)` ta có dãy tỉ số bằng nhau `: x/10=y/15 = x/21`

Áp dụng tính chất dãy tỉ số bằng nhau ta được `:`

`x/10=y/15 = x/21` `= ( x + y + z )/( 10 + 15 + 21 ) = 92/46 = 2` 

`->` `{(x/10=2),(y/15=2),(z/21=2):}`

`-> {(x=20),(y=20),(z=42):}`

Vậy `....` 

x/2 = y/3

=> x.5/2.5 = y.5/3.5

=> x/10=y/15

y/5 = z/7 

=> y.3/5.3= z.3/7.3

=> y/15 = z/21

x/10=y/15; y/15=z/21

Nên suy ra ta được :

     x/10= y/15=z/21

x+y+x/10+15+21

=> 92/46= 2

=> x= 10.2= 20

=> y= 15.2=30

=> z= 21.2=42

Bạn tham khảo nhé !

Ta có:

\(m=2^3.3.7^5\)

\(n=5.11^3.3^4\)

\(\Rightarrow BCNN\left(m;n\right)=2^3.3^4.5.7^5.11^3\)

1.

a{ W ; I ; F ; I }

2.

B { 4 ; 6 ; 9 ; 11}

1. A = {W,I,F}

2.

a) B = {tháng 4; tháng 6; tháng 9; tháng 11}

b) quý mấy bạn? 

`a)35+51+65+49`

`=(35+65)+(51+49)`

`=100+100`

`=200`

`b)(205+196)+104`

`=205+(196+104)`

`=205+200`

`=405`

Tính nhanh các giá trị biểu thức sau

a) 35 + 51 + 65 + 49

= (35 + 65) + (51 + 49)

= 100 + 100

= 200

b) (205 + 196) + 104

= 401 + 104

= 505.