\(2x^5+2=4\\ 2x^5=2\\ x^5=1\\ x=1\)

a, x ∈ B(12) 

B(12) = {0;12;24;36;48;60;84;96;108;.........}

Vì \(x\le100\)

=> \(x\in\left\{\text{0;12;24;36;48;60;84;96}\right\}\)

b, x ∈ Ư(20)

Ư(20) = {1;2;5;4;10;20}

Vì x > 8 

=> x ∈ {10;20}

c. x ∈ B(8)

B(8) = {0;8;16;24;32;40;48;56;64;72;80;.......;120;128}

Vì \(12\le x\le120=>x\in\left\{16;24;32;......;120\right\}\)

d. x ∈ Ư(45)

Ư(45) = {1;5;3;9;15;45}

vì x > 5 => x ∈ {9;15;45}

\(b.75\%-1\dfrac{2}{3}+0,5:\dfrac{5}{12}\)

\(=\dfrac{3}{4}-\dfrac{5}{3}+\dfrac{6}{5}\)

\(=\dfrac{17}{60}\)

\(d.\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+....+\dfrac{1}{399}+\dfrac{1}{483}\)

\(=\left(\dfrac{2}{3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+.....+\dfrac{2}{21\cdot19}+\dfrac{2}{21\cdot23}\right)\cdot\dfrac{1}{2}\)

\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{23}\right)\cdot\dfrac{1}{2}\)

\(=\left(1-\dfrac{1}{23}\right)\cdot\dfrac{1}{2}\)

\(=\dfrac{22}{23}\cdot\dfrac{1}{2}\)

\(=\dfrac{11}{23}\)

3. 

\(C=5+5^2+...+5^6\\ C=5\left(1+5\right)+5^3\left(1+5\right)+5^5\left(1+5\right)\\ C=5\cdot6+5^3\cdot6+5^5\cdot6\\ C=6\left(5+5^3+5^5\right)\\ =>C⋮6\)

\(4.D=3+3^2+...+3^6\\D=3\left(1+3\right)+3^3\left(1+3\right)+3^5\left(1+3\right)\\ D=3\cdot4+3^3\cdot4+3^5\cdot5\\ C=4\left(3+3^3+3^5\right)\\ =>D⋮4\\ 5.E=4+4^2+...+4^6\\ E=4\left(1+4\right)+4^3\left(1+4\right)+4^5\left(1+4\right)\\ E=4\cdot5+4^3\cdot5+4^5\cdot5\\ E=5\left(4+4^3+4^5\right)=>E⋮5 \)

16) -9/13 . 5/17 + (-17/13) . 5/17

= (-9/13 - 17/13) . 5/17

= -2 . 5/17

= -10/17

17) 7/15 . (-4/9) + (-5/9) . 7/15

= 7/15 . (-4/9 - 5/9)

= 7/15 . (-1)

= -7/15

18) 3/8 . (-23/14) - 3/8 . (-9/14)

= 3/8 . (-23/14 + 9 /14)

= 3/8 . ( -1)

= -3/8

13) -2/3 . 3/11 + (-16/9) . 3/11

= 3/11 . (-2/3 - 16/9)

= 3/11 . (-22/9)

= -2/3

14) -5/9 . 3/11 + (-13/18) . 3/11

= 3/11 . (-5/9 - 13/18)

= 3/11 . (-23/9)

= -23/33

15) 2/13 . (-5/3) + 11/13 . (-5/3)

= -5/3 . ( 2/13 + 11/13)

= -5/3 . 1

= -5/3 

10) 7/15 . 16/13 + 7/15 . (- 3/13)

= 7/15 . (16/13 - 3/13)

= 7/15 . 1

= 7/15

11) -23/7 . 3/10 + 13/7 . 3/10

= 3/10 . (-23/7 + 13/7)

= 3/10 . (- 10/7)

= -3/7

12) -11/8 . 19/3 + 19/3 . -5/8

= 19/3 . ( -11/8 - 5/8)

= 19/3 . (-2)

= -38/3

7) 2/7 . 8/19 + 5/7 . 8/19

= 8/19 . ( 2/7 + 5/7)

= 8/19 . 1

= 8/19

8) 23/15 . 3/8 - 17/15 . 3/8

= 3/8 . ( 23/15 - 17/15)

 = 3/8 . 2/5

= 3/20

9) 3/2 . 5/3 - 7/6 . 3/2

= 3/2 . (5/3 - 7/6) 

= 3/2 . 1/2

= 3/4

4) 7/2 . 11/6 - 7/2 . 5/6

= 7/2 . (11/6 - 5/6)

= 7/2 . 1

= 7/2

5) 11/9 . 3/4 - 2/9 . 3/4

= 3/4 . (11/9 - 2/9)

= 3/4 . 1

= 3/4

6) 3/7 . 13/5 + 3/7 . 8/5

= 3/7 . (13/5 + 8/5)

= 3/7 . 21/5

= 9/5

1) 2/5 . 3/8 + 5/8 . 2/5

= 2/5 . ( 3/8+5/8)

= 2/5 . 1

= 2/5

2) 2/3 . 5/2 - 3/4 . 2/3

= 2/3 . (5/2-3/4)

= 2/3 . (10/4-3/4)

= 2/3 . 7/4

= 7/6

3) 5/7 . 19/23 - 12/23 . 5/7

= 5/7 . (19/23 - 12/23)

= 5/7 . 7/23

= 5/23

3)