\(a,\left(x+2\right)^2+\left(x+3\right)^2-2\left(x-2\right)\left(x-3\right)=19\\ \Leftrightarrow x^2+4x+4+x^2+6x+9-2x^2+10x-12=19\\ \Leftrightarrow20x=20\\ \Leftrightarrow x=1\\ b,\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-5\right)=15\\ \Leftrightarrow x^3+8-x^3+5x=15\\ \Leftrightarrow5x=7\\ \Leftrightarrow x=\dfrac{7}{5}\\ c,\left(x-1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=17\\ \Leftrightarrow x^3-3x^2+3x+1+8-x^3+3x^2+6x=17\\ \Leftrightarrow9x=8\\ \Leftrightarrow x=\dfrac{8}{9}\)

a. (x + 2)² + (x + 3)² - 2(x - 2)(x - 3) = 19

<=> (x² + 4x + 4) + (x² + 6x + 9) - (2x + 4)(x - 3) = 19

<=> x² + 4x + 4 + x² + 6x + 9 - 2x² + 6x - 4x + 12 = 19

<=> x² + x² - 2x² + 4x + 6x + 6x - 4x + 9 + 4 + 12 - 19 = 0

<=> 12x + 6 = 0

<=> 6(2x + 1) = 0

<=> 2x + 1 = 0

<=> 2x = -1

<=> x = \(\dfrac{-1}{2}\)  

Bài 22:

a: =>-12x+60+21-7x=5

=>-19x+81=5

=>-19x=-76

=>x=4

b: =>30x+60-6x+30-24x=100

=>90=100(loại)

Bài 2: 

a: \(A=\left(x+1\right)^3+5=20^3+5=8005\)

b: \(B=\left(x-1\right)^3+1=10^3+1=1001\)

a,  2x+15=67-(-18)                                   b, 4x-12=3x-(-7)                                               c, 2|x-1|+3=13

   2x+15=67+18                                          4x-12=3x+7                                                     2|x-1|    = 13-3

   2x+15=  85                                             4x-3x = 12+7                                                   2|x-1|    =10

   2x     =85-15                                           x      = 19                                                        |x-1|      = 10:2

   2x     =  70                                                                                                                    |x-1|      =   5

    x      = 70:2                                                                                                                  +) Nếu x=5 thì x-1=5 suy ra x=6

   x       =  35                                                                                                                    +) Nếu x=-5 thì x-1= -5 suy ra x= -4

a, 2x + 15 = 67-(-18)

=> 2x + 15 = 67 + 18

=> 2x = 85 - 15

=> 2x = 70

=> x = 35

b, 4x - 12 = 3x-(-7)

=> 4x - 12 = 3x + 7

=> 4x - 3x = 7 + 12 

=> x = 19

c, 2|x - 1| + 3 = 13

=> 2|x - 1| = 10

=> |x - 1| = 5

=> x - 1 = 5 hoặc x - 1 = -5

=> x = 6 hoặc x = -4

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}

x=1

x=-1

a)  3x – 15 = 25 – 5x 

=> 3x + 5x = 25 + 15

=> 8x = 40

=> x = 5

 b) 3x - 17 = 2x – 7     

=> 3x - 2x = -7 + 17

=> x = 10

 c) 2x – 17 =  – (3x – 18)

=> 2x - 17 = -3x + 18

=> 2x + 3x = 18 + 17

=> 5x = 35

=> x = 7

d) 3x – 14 = 2(x – 9) + 1

=> 3x - 14 = 2x - 18 + 1

=> 3x - 2x = -18 + 1 + 14

=> x = -3

f) (x – 5)² = 9          

\(\Rightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

a) Ta có: \(3x-15=25-5x\)

\(\Leftrightarrow3x-15-25+5x=0\)

\(\Leftrightarrow8x-40=0\)

\(\Leftrightarrow8x=40\)

hay x=5

Vậy: x=5

b) Ta có: \(3x-17=2x-7\)

\(\Leftrightarrow3x-17-2x+7=0\)

\(\Leftrightarrow x-10=0\)

hay x=10

Vậy: x=10

c) Ta có: \(2x-17=-\left(3x-18\right)\)

\(\Leftrightarrow2x-17=-3x+18\)

\(\Leftrightarrow2x-17+3x-18=0\)

\(\Leftrightarrow5x-35=0\)

\(\Leftrightarrow5x=35\)

hay x=7

Vậy: x=7

d) Ta có: \(3x-14=2\left(x-9\right)+1\)

\(\Leftrightarrow3x-14=2x-18+1\)

\(\Leftrightarrow3x-14-2x+18-1=0\)

\(\Leftrightarrow x+3=0\)

\(\Leftrightarrow x=-3\)

Vậy: x=-3

f) Ta có: \(\left(x-5\right)^2=9\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

Vậy: \(x\in\left\{2;8\right\}\)

a)   x + 118 = 218

x = 218 – 118

x = 100

b)   18 – x = -17

X = 18 – (-17)

X = 35

c)    (-18) – x = -17

X = (-18) – (-17)

X = -1

d)124 + (118 – x) = 217

118 – x = 93

X = 118 – 93

X = 25

e) (3x – 6).3 = 3⁴

(3x – 6).3 = 81

3x – 6 = 27

3x = 33

ð X = 11

g) 23.(42 – x) = 46

42 – x = 2

ð X = 40

h) 84 – (3x + 8) = 34

3x + 8 = 84 – 34

3x + 8 = 50

3x = 50 – 8

3x = 42

X = 42 : 3

ð X = 14

i)               3.(2x + 1) – 19 = 14

3.(2x + 1) = 14 + 19

3.(2x + 1) = 33

2x + 1 = 33 : 3

2x + 1 = 11

2x = 11 – 1

2x = 10

X = 10 : 2

ð X = 5

k) 6x – 302 = 2³.5

6x – 302 = 40

6x = 40 + 302

6x = 342

X = 342 : 6

ð X = 57

m) (x – 1)² = 81

(x – 1)² = 9²

ð X – 1 = 9

ð X = 9 + 1

ð X = 10

n) 2^x+1 – 5 = 27

2^x+1 = 27 + 5

2^x+1 = 32

2^x+1 = 2⁵

ð X = 4

a) x = 3

b) x = 53

c) x = 2024

d) x = 6