A=2+2\(^2\)+2\(^3\)+...+2\(^{100}\)= (2+2\(^2\))+(2\(^3\)+2\(^4\))+...+(2\(^{99}\)+2\(^{100}\))

  =(2+2\(^2\))+2\(^2\).(2+2\(^2\))+2\(^4\).(2+2\(^2\))+...+2\(^{98}\).(2+2\(^2\))

  =6+6.2\(^2\)+6.2\(^4\)+...+6.2\(^{98}\)=6.(1+2\(^2\)+2\(^4\)+...+2\(^{98}\))\(⋮\)6

  =>A\(⋮\)2

\(\frac{-3}{2}\left(5-\frac{1}{6}\right)+4\left(x-\frac{1}{2}\right)=\frac{1}{2}+x\)

\(\Leftrightarrow\frac{-29}{4}+4x-2=\frac{1}{2}+x\)

\(\Leftrightarrow\frac{-37}{4}+4x=\frac{1}{2}+x\)

\(\Leftrightarrow4x-x=\frac{1}{2}+\frac{37}{4}\)

\(\Leftrightarrow3x=\frac{39}{4}\)

\(\Leftrightarrow x=\frac{13}{4}\)

Vậy \(x=\frac{13}{4}\)

Ta có:\(a=75.30^n=3.5^2.2^n.3^n.5^n=2^n.3^{n+1}.5^{n+2}\)

Số ước của a bằng:

\(\left(n+1\right)\left[\left(n+1\right)+1\right]\left[\left(n+2\right)+1\right]=\left(n+1\right)\left(n+2\right)\left(n+3\right)\)

Mà a có 1030200 ước

Suy ra\(\left(n+1\right)\left(n+2\right)\left(n+3\right)=1030200=100.101.102\)

                 \(\Leftrightarrow n=99\)

Thay n=99 vào a ta được:

\(a=75.30^{99}=\)

a) Ta có: x + 1 = (x - 3) + 4

Do x - 3 \(⋮\)x - 3 => 4 \(⋮\)x - 3

     => x - 3 \(\in\)Ư(4) = {1; -1; 2; -2; 4; -4}

Lập bảng :

Vậy ...

b) Ta có: x² - 3  = x(x + 1) - x - 3 = x(x + 1) - (x + 1) - 2 = (x - 1)(x + 1) - 2

Do (x - 1)(x + 1) \(⋮\)x + 1 => 2 \(⋮\)x + 1

     => x + 1 \(\in\)Ư(2) = {1; -1; 2; -2}

Với : x + 1 = 1 => x = 0

       x + 1 = -1 = > x = -2

     x + 1 = 2 => x = 1 

        x + 1 = -2 => x = -3

Vậy ...

a. \(\left(x+1\right)⋮\left(x-3\right)\)

\(\Rightarrow\left(x-3\right)+4⋮\left(x-3\right)\)

Vì \(\left(x-3\right)⋮\left(x-3\right)\)

\(\Rightarrow4⋮\left(x-3\right)\)

\(\Rightarrow\left(x-3\right)\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

\(\Rightarrow x\in\left\{2;4;1;5;-1;7\right\}\)

mk chỉ làm đc câu a thôi, thông cảm nha

\(2\left(\frac{3}{2}-x\right)-\frac{1}{3}=7x-\frac{1}{4}\)

\(\Leftrightarrow3-2x-\frac{1}{3}=7x-\frac{1}{4}\)

\(\Leftrightarrow2x-\left(-3+\frac{1}{3}\right)=7x-\frac{1}{4}\)

\(\Leftrightarrow2x-\left(-\frac{9}{3}+\frac{1}{3}\right)=7x-\frac{1}{4}\)

\(\Leftrightarrow2x-\left(-\frac{8}{3}\right)=7x-\frac{1}{4}\)

\(\Leftrightarrow2x+\frac{8}{3}=7x-\frac{1}{4}\)

\(\Leftrightarrow2x-7x=-\frac{8}{3}-\frac{1}{4}\)

\(\Leftrightarrow-5x=-\frac{32}{12}-\frac{4}{12}\)

\(\Leftrightarrow-5x=-3\)

\(\Leftrightarrow x=\left(-3\right):\left(-5\right)\)

\(\Leftrightarrow x=\frac{3}{5}\)

\(2\left(\frac{3}{2}-x\right)-\frac{1}{3}=7x-\frac{1}{4}\)

\(3-2x-\frac{1}{3}\)\(=7x-\frac{1}{4}\)

\(-2x-7x=-\frac{1}{4}-3+\frac{1}{3}\)

\(-9x=-\frac{35}{12}\)

\(x=-\frac{35}{12}:\left(-9\right)\)

\(x=\frac{35}{108}\)

Vậy \(x=\frac{35}{108}\)

\(S=1+3+\cdot\cdot+3^{99}\)

\(\Rightarrow3S=3+3^2+\cdot\cdot\cdot+3^{100}\)

\(\Rightarrow3S-S=\left(3+\cdot\cdot\cdot+3^{100}\right)-\left(1+3+\cdot\cdot\cdot+3^{99}\right)\)

\(\Rightarrow2S=3^{100}-1\)

\(\Rightarrow2S+1=3^{100}\)

Chứng tỏ 2S +1 là luỹ thừa của 3

25+1=26 làm sao là lũy thừa của 3 đc!

Chắn đề sai rùi bn ạ,bn nhìn lại đề xem!

#Hok_tốt

=>2/9*(x-9/4)+1/2=41/14+1/3

=>2/9*(x-9/4)=137/42-1/2

=> x-9/4=58/21:2/9

=>x=87/7+9/4

=>x=411/28

  nếu sai thì trách cái máy tính chứ đừng có trách mk

T lười chép đề bài lắm :)

\(\frac{2}{9}\cdot\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{3}{7}\cdot\frac{41}{6}+\frac{1}{3}\)

\(\frac{2}{9}\cdot\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{41}{14}+\frac{1}{3}\)

\(\frac{2}{9}\cdot\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{137}{42}\)

\(\frac{2}{9}\cdot\left(x-\frac{9}{4}\right)=\frac{137}{42}-\frac{1}{2}\)

\(\frac{2}{9}\cdot\left(x-\frac{9}{4}\right)=\frac{58}{21}\)

\(x-\frac{9}{4}=\frac{58}{21}:\frac{2}{9}\)

\(x-\frac{9}{4}=\frac{87}{7}\)

\(x=\frac{87}{7}+\frac{9}{4}\)

\(x=\frac{411}{28}\)

Vậy ...

P/s : Chả bt có đúng k :> 

1,\(\frac{2}{9}.\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{3}{7}.\left(7-\frac{1}{6}\right)+\frac{1}{3}\)

  \(\frac{2}{9}.\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{3}{7}.\frac{41}{6}+\frac{1}{3}\)

\(\frac{2}{9}.\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{41}{14}+\frac{1}{3}\)

 \(\frac{2}{9}.\left(x-\frac{9}{4}\right)+\frac{1}{2}=\frac{137}{42}\)

\(\frac{2}{9}.\left(x-\frac{9}{4}\right)=\frac{137}{42}-\frac{1}{2}\)

\(\frac{2}{9}.\left(x-\frac{9}{4}\right)=\frac{58}{21}\)

 \(\left(x-\frac{9}{4}\right)=\frac{5}{2}:\frac{2}{9}\)

\(\left(x-\frac{9}{4}\right)=\frac{45}{4}\)

\(x=\frac{45}{4}+\frac{9}{4}\)

\(x=\frac{27}{2}\)

Bước cưối 58/21 minh man viết nhầm nên sai 

số cốc trà sữa là 120 vì từ 116 đến 123 thì có 116 và 120 nhưng lớn hơn 116 nên là chỉ có 120

DS là 120