a: \(2^3-5^3:5^2+12\cdot2^2\)

\(=8-5+48\)

\(=51\)

b: \(5\cdot\left[\left(85-35:7\right):8+90\right]-5\)

\(=5\cdot\left[10+90\right]-5\)

=495

a: 23−53:52+12⋅2223−53:52+12⋅22

=8−5+48=8−5+48

=51=51

b: 5⋅[(85−35:7):8+90]−55⋅[(85−35:7):8+90]−5

=5⋅[10+90]−5=5⋅[10+90]−5

=495

a) (3⁵ . 3⁷) : 3¹⁰ + 5 . 2⁴ - 7³ : 7

= 3¹² : 3¹⁰ + 5.16 - 7²

= 3² + 80 - 49

= 9 + 31

= 40

b) (7⁵ + 7⁹) . (5⁴ + 5⁶) . (3³.3 - 9²)

= (7⁵ + 7⁹) . (5⁴ + 5⁶) . (81 - 81)

= (7⁵ + 7⁹) . (5⁴ + 5⁶) . 0

= 0

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

siuu

Bài 1

S₂ = 21 + 23 + 25 + ... + 1001

Số số hạng của S₂:

(1001 - 21) : 2 + 1 = 491

⇒ S₂  = (1001 + 21) . 491 : 2 = 250901

--------

S₄  = 15 + 25 + 35 + ... + 115

Số số hạng của S₄:

(115 - 15) : 10 + 1 = 11

⇒ S₄ = (115 + 15) . 11 : 2 = 715

Bài 2

a) 2x - 138 = 2³.3²

2x - 138 = 8.9

2x - 138 = 72

2x = 72 + 138

2x = 210

x = 210 : 2

x = 105

b) 5.(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 78

c) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305

x = 407

d) 20 - [7.(x - 3) + 4] = 2

7(x - 3) + 4 = 20 - 2

7(x - 3) + 4 = 18

7(x - 3) = 18 - 4

7(x - 3) = 14

x - 3 = 14 : 7

x - 3 = 2

x = 2 + 3

x = 5

e) 9ˣ⁻¹ = 9

x - 1 = 1

x = 1 + 1

x = 2

a)73+86+968+914+3032

= (86 + 914) +(968 + 3032) + 73

= 1000 + 4000 + 73

= 5073

b)341.67+341.16+659.83

=341 (67 + 16) + 659 * 83

= 341 * 83 + 659 * 83

= (341+ 659) * 83

= 1000 * 83

= 830000

c)252-84:21+7

= 252 - 2 +7

=257

d)4.8.25.125.27

= (8 * 125) (4* 25) * 27

= 1000 * 100 * 27

= 2700000

e)34+35+36+37-24-25-26-27

= (34-24) + (35-25) + (36-26) + (37-27)

= 10 + 10 + 10 + 10

= 40

g)1-2+3-4+...-98+99

= (1 + 99) + (-2-98) + .....+ (-48 - 52) + (49 + 51) - 50

= 100 - 50

= 50

h)1-4+7-10+...-100+103

Bài 2:Tìm số nguyên x,biết:

l)3636:(12.x-91)=36

3636 : (12x - 91) = 36

12x - 91 = 101 

12x = 192

x= 16 

m)(x:23+45).67=8911

x: 23 + 45 = 133

x : 23 = 88

x= 88/23

n)[(6.x-39):7].4=12

6x - 39 = 3

6x = 42

x=7

p)128-3(x+4)=23

3(x+4) = 105

x+4= 35

x= 31

q)[(4.x+28).3+55]:5=35

(4x + 28)*3 +55 = 175

(4x + 28) * 3 = 120

4x + 28 = 40

4x = 12

x=3

r)123-5.(x+4)=38

5(x+4) = 85

x+4 = 17 

x= 13 

t)11-(53+x)=97

53 + x = -86

x= -139

i)23.75+25.23+180

= 23(75+25) + 180

= 2300 + 180 

= 2480 

https://friend20.com/vn/d20/quiz/69707687

Hoctot

1) (x - 35) - 120 = 0

x - 35 = 120

x = 120 + 35

x = 155

2) 310 - (118 - x) = 217

118 - x = 310 - 217

118 - x = 93

x = 118 - 93

x = 25

3) 156 - (x + 61) = 82

x + 61 = 156 - 82

x + 61 = 74

x = 74 - 61

x = 13

4) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305 = 407

5) 100 - 7 - (x - 5) = 58

x - 5 = 93 - 58

x - 5 = 35

x = 35 + 5 = 40

6) 12(x - 1) : 3 = 4³ + 2³

4(x - 1) = 72

x - 1 = 18

x = 18 + 1 = 19

7) 24 + 5x = 7⁵ : 7³

24 + 5x = 49

5x = 25

x = 25 : 5 = 5

8) 5(x - 1) : 3 = 4³ + 2³

\(\dfrac{5}{3}\left(x-1\right)=72\)

x - 1 = \(\dfrac{216}{5}\)

x = 221/5

9) 5(x - 4)² - 7 = 13

5(x - 4)² = 20

(x - 4)² = 4

\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\)   \(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)

10) (x + 1) + (x + 2) + ... + (x + 30) = 795

=> (x + x + x + ... + x) + (1 + 2 + 3 +...+ 30) = 795 (1)

Đặt A = 1 + 2 + 3 +...+ 30

Số số hạng trong A là: (30 - 1) : 1 + 1 = 30 (số)

Tổng A bằng : (30 + 1).30 : 2 =465

Thay A = 465 vào (1) , ta được:

30x + 465 = 795

=> 30x =330

=> x =11

1: =>x-35=120

=>x=120+35=155

2: =>118-x=310-217=93

=>x=118-93=25

3: =>x+61=156-82=74

=>x=74-61=13

4: =>x-305=814-712=102

=>x=102+305=407

5: =>93-(x-5)=58

=>x-5=35

=>x=40

6: =>4(x-1)=64+8=72

=>x-1=18

=>x=19

7: =>5x+24=49

=>5x=25

=>x=5

8: =>5(x-1):3=4^3+2^3=64+8=72

=>5(x-1)=216

=>x-1=216/5

=>x=221/5

4.x=16

-37 + 14 +26 + 37 

=-37 + 37 + 14 + 36 

=0 + 50

=50

  -24 + 6 + 10 + 24 

=(-24 + 24) +(6+10)

= 0+16

= 16

các bạn viết cả cách làm cho mình nhé