a)19 - (x + 2³)=2⁴- 6

   19 - (x + 2³) = 16 - 6 

    19 - (x + 2³) = 10

     (x + 2³) = 19 - 10

      x + 2³= 9

      x + 2³ = 3³

      ^{x + 2 = 3}

      ^{x= 3-2}

       ^{x= 1}

sửa lại :

a)19 - (x + 2³)=2⁴- 6

   19 - (x + 2³) = 16 - 6 

    19 - (x + 2³) = 10

     (x + 2³) = 19 - 10

      x + 2³= 9

    =>  x + 8= 9             x= 1

      ^{=> x + 8 =-9                     x= -17}

a) 23 + 25 + 27 + 29 + 31 + 33 + 35

= 23 + ( 25 + 35 ) + ( 27 + 33 ) + ( 29 + 31 )

= 23 +        60      +      60         +      60

= 23 + 60 x 3

= 23 +    180

= 203

b) 4 . 36 . 25 . 50

=  4 . 4 .9 . 25 . 25 . 2

= 4 . 25 . 4 . 25 . 9 . 2

=   100 . 100     . 9 . 2

= 10 000           . 18

= 180 000

c) 32 . 125 . 3 

= 4 . 8 . 5 . 25 . 3

= 4 . 25 . 8 . 5 . 3

=  100    . 8 . 5 . 3

=      800 . 5 . 3

= 4000 . 3

= 12000

d, 36 . 19 + 36 . 81

= 36 . ( 19 + 81 )

= 36 . 100

= 3600

e, 78 . 31 + 78 . 24 + 78 . 17 + 22 x 72

= 78 . ( 31 + 24  + 17 ) + 22 x 72

= 78 . 72 + 22 . 72

= 72 . ( 78 + 22 )

= 72 . 100

= 7200

A)23+25+27+29+31+33+35

= (33+27)+(25+35)+(29+31)+23

=60+60+60+23

=60x3+23

=180+23

=203

B)4.36.25.50=(36.25).(4.50)

=(4.9.25).(2.2.50)

=(4.25).9 .(2.50).2

=100.9.100.2

=100.(9+2)

=100 .11

=1100

C)32.125.3=(4.8).125.3

=(125.8).(4.3)

=1000.12

=12000

D)36.19.36.81=36.(19+81)

 = 36.100

=3600

E)78.31.+78.24+78.17+22x72=78.31+78.24+78.17+ (16+6).72

=78.31+78.24+78.17+78.16

=78.(31+24+17+16)

=78.88

=6864

C1:

a. 786 x ( 32 +68)

= 786 x  100

= 78600

b. 2904 x 15 + 2904 x 35

= 43560 + 101640

= 145200

c.436 x 72 - 436 x 42

= 31392 - 18312

= 13080

d.194 x (87-7)

= 194 x 80

=15520

e.3332 : (4x49)

= 3332 : 196

= 17

f. 72 : 9 : 8

= (72 : 9) :8

= 1

g. (15 x 24) : 6

= 360 :6

= 60

m. 25 x(36 :9)

= 25 x 4

= 100

Cách 2:

a.786 x 32 + 786 x 68

= 25152 + 53448

= 78600

b. 2904 x ( 15 + 35)

= 2904 x 50

= 145200

c.436 x (72 -42)

= 436 x 30

= 13080

d.194 x 87 - 194 x7

= 16878 - 1358

= 15520

e. 3332 : (4 x 49)

= 3332 : 4 : 49

= 833 : 49 = 17

f. 72 : 9 :8

= 72 : (9 x8)

= 72 : 72

=1

g. (15 x 24) :6 

= 15 x (24 :6)

= 15 x 4

= 60

m. 25 x (36 :9)

= ( 25 x36 ):9

= 900 : 9

=100

a: \(280-\left(x-140\right):35=270\)

=>(x-140):35=280-270=10

=>x-140=350

=>x=350+140

=>x=490

b: \(\left(190-2x\right):35-32=16\)

=>\(\left(190-2x\right):35=32+16=48\)

=>\(190-2x=35\cdot48=1680\)

=>2x=190-1680=-1490

=>x=-745

c: \(720:\left\lbrack41-\left(2x-5\right)\right\rbrack=2^3\cdot5\)

=>\(720:\left\lbrack41-\left(2x-5\right)\right\rbrack=8\cdot5=40\)

=>41-(2x-5)=720:40=18

=>2x-5=41-18=23

=>2x=28

=>x=14

d: \(\left(x:23+45\right)\cdot37-22=2^4\cdot105\)

=>\(\left(\frac{x}{23}+45\right)\cdot37=16\cdot105+22=1702\)

=>\(\frac{x}{23}+45=46\)

=>\(\frac{x}{23}=1\)

=>x=23

e: \(\left(3x-4\right)\left(x-1\right)^3=0\)

=>\(\left[\begin{array}{l}3x-4=0\\ x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac43\\ x=1\end{array}\right.\)

f: \(2^{2x-1}:4=8^3\)

=>\(2^{2x-1-2}=2^9\)

=>2x-3=9

=>2x=12

=>x=6

g: \(x^{17}=x\)

=>\(x^{17}-x=0\)

=>\(x\left(x^{16}-1\right)=0\)

=>\(\left[\begin{array}{l}x=0\\ x^{16}-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x^{16}=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\\ x=-1\end{array}\right.\)

h: \(\left(x-5\right)^4=\left(x-5\right)^6\)

=>\(\left(x-5\right)^6-\left(x-5\right)^4=0\)

=>\(\left(x-5\right)^4\cdot\left\lbrack\left(x-5\right)^2-1\right\rbrack=0\)

=>\(\left(x-5\right)^4\cdot\left(x-4\right)\left(x-6\right)=0\)

=>x∈{4;5;6}

i: \(\left(x+2\right)^5=2^{10}\)

=>\(\left(x+2\right)^5=\left(2^2\right)^5=4^5\)

=>x+2=4

=>x=2

k: 1+2+3+...+x=78

=>\(\frac{x\left(x+1\right)}{2}=78\)

=>x(x+1)=156

=>\(x^2+x-156=0\)

=>(x+13)(x-12)=0

=>x=-13(loại) hoặc x=12(nhận)

l: \(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)

=>\(3x-16=2\cdot\frac{7^4}{7^3}=2\cdot7=14\)

=>3x=16+14=30

=>\(x=\frac{30}{3}=10\)

n: \(5^{x}:5^2=125\)

=>\(5^{x-2}=5^3\)

=>x-2=3

=>x=5

m: \(\left(x+1\right)^2=\left(x+1\right)^0\)

=>\(\left(x+1\right)^2=1\)

=>\(\left[\begin{array}{l}x+1=1\\ x+1=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-2\end{array}\right.\)

o: Số số hạng của dãy số 2;4;..;52 là:

(52-2):2+1=50:2+1=25+1=26(số)

Tổng của dãy số 2;4;...;52 là:

\(\left(52+2\right)\cdot\frac{26}{2}=54\cdot13=702\)

(2+x)+(4+x)+...+(52+x)=780

=>26x+702=780

=>26x=78

=>x=3

p: \(70=2\cdot5\cdot7;80=2^4\cdot5\)

=>ƯCLN(70;80)=\(2\cdot5=10\)

70⋮x; 80⋮x

=>x∈ƯC(70;80)

=>x∈Ư(10)

mà x>8

nên x=10

q: \(12=2^2\cdot3;25=5^2;30=2\cdot3\cdot5\)

=>BCNN(12;25;30)=\(2^2\cdot3\cdot5^2=300\)

x⋮12; x⋮25; x⋮30

=>x∈BC(12;25;30)

=>x∈B(300)

mà 0<x<500

nên x=300

2.

a, x-13=-46

=>x=(-46)+13

=>x=33

b, 4x-6=22

=>4x=22+6

=>4x=28

=>x=28:4

=>x=7

3.

a, 32=2⁵

48=2⁴.3

=>ƯCLN(32,48)=2⁴=16

16=2⁴

72=2³.3²

=>ƯCLN(16,72)=2³=8

b,

24=2³.3

60=2².3.5

=>BCNN(24,60)=2³.3.5=120

72=2³.3²

180=2².3².5

=>BCNN(72,180)=2³.3².5=360

a) x - 13  =  -   46 

    x         =  - ( 46 + 13 )                                

    x         =  - 59   

Chắc vậy

bài 2 tìm x

a,106- ( x+ 7) =9

x+7 = 106 - 9

x+7 = 107

x= 107 - 7

x=100

b, 2 x ( x+ 4) + 5 =65

2 x (x+4) = 65 - 5

2 x (x+4) = 60

x+4 = 60:2

x+4= 30

x= 30 - 4

x=26

c, (16x x -32) x 45=0

16 x X - 32 = 0: 45

16 x X - 32 =0

16 x X = 0 + 32

16 x X = 32

X= 32:16

X=2

d, x+4 x x = 100 : 5

X + 4 x X = 20

(1+4) x X = 20

5 x X  = 20

X= 20:5

X=4

Bài 1:

a, 24 x 66 - 24 + 36 x 24

= 24 x (66-1+36)

= 24 x 101

= 24 x 100 + 24

= 2400+24

=2424

b, 29 x 173 - 29 x 72 - 29

= 29 x (173 - 72 -1)

= 29 x 100

= 2900

c, 1+5+10+15+...+55+60

= (5+60) x 6 + 1 (có 6 cặp)

= 65 x 6 + 1

= 390 +1 =391

d, D= 1 x 2 + 2 x 3 + 3 x 4 +...+18 x 19 + 19 x 20

3D= 1 x 2 x 3+ 2 x 3 x (4-1) + 3 x 4 x (5-2) +...+ 18 x 19 x (20 - 17) + 19 x 20 x (21-18)

3D= 1 x 2 x 3 - 1 x 2 x 3 + 2 x 3 x 4 - 2 x 3 x 4 +.... + 19 x 20 x 21 - 18 x 19 x 20

3D= 19 x 20 x 21 =7980

=> D= 7980:3=2660

18 - 4\(x\) = -20 - 6\(x\) 

-4\(x\) + 6\(x\) = - 20  - 18

      2\(x\)    = - 38

         \(x\)  = - 19

h, -15 \(\times\) 24 = -7\(x\) + 32

     7\(x\) = 360 + 32

      7\(x\) = 392

         \(x\) =  392:7

          \(x\) = 56

i, 15\(x\) -3.(4\(x\) - 6) = -12 + 36

    15\(x\) - 12\(x\) + 18 =  24

      3\(x\) = 24 - 18

       3\(x\) = 6

         \(x\) = 2

k, -10\(x\) - 27 = -7\(x\) + 33

    -27 - 33 = -7\(x\) + 10\(x\)

     3\(x\) = -60

        \(x\) = -20

a) 24 = 2³ . 3

36 = 2² . 3³

ƯCLN(24,36) = 2² . 3 = 4 . 3 = 12

b) 32 = 2⁵

48 = 2⁴ . 3 

ƯCLN(32,48) = 2⁴ = 16

c) 24 = 2³ . 3

84 = 2² . 3 . 7

180 = 2² . 3² . 5

ƯCLN(24,84,180) = 2² . 3 = 4 . 3 = 12

1)

a) 2x + 5 = 3⁴ : 3²

2x + 5 = 3²

2x + 5 = 9

2x = 9 - 5

2x = 4

x = 4 : 2

x = 2

b) (3x - 24).73 = 2.74

(3x - 24).73 = 148

3x - 24 = 148/73

3x = 148/73 + 24

3x = 1900/73

x = 1900/73 : 3

x = 1900/219

c) [3.(42 - x)] + 15 = 23.3

126 - 3x + 15 = 69

141 - 3x = 69

3x = 141 - 69

3x = 72

x = 72 : 3

x = 24

d) 126 + (132 - x) = 300

132 - x = 300 - 126

132 - x = 174

x = 132 - 174

x = -42

2)

a) 120 - (x + 55) = 60

x + 55 = 120 - 60

x + 155 = 60

x = 60 - 55

x = 5

b) (7x - 11).3 = 25.52 + 200

(7x - 11).3 = 1500

7x - 11 = 1500 : 3

7x - 11 = 500

7x = 500 + 11

7x = 511

x = 511 : 7

x = 73

c) 2x + 2x + 4 = 544

4x = 544 - 4

4x = 540

x = 540 : 4

x = 135