a: =>x-8=27

hay x=35

a. 25 + 3(x-8) = 106

3(x-8) = 106 - 25 = 81

x -8 = 81 : 3 = 27

x = 27 +8 = 35

b. 3²(x +4) - 5² = 5.5²

9(x+4) - 25 = 5.25 = 125

9(x+4) = 125 + 25 = 150(Đề sai)

3.(x-8) = 106-25

3.(x-8) = 81

x-8 = 81:3

x-8 = 27

x=35

\(a,25+3\left(x-8\right)=106\\ 3\left(x-8\right)=81\\ x-8=27\\ x=35\)

3² . (x + 4 ) - 5² = 5 . 2²

9  . ( x + 4 ) - 25 = 20

9 . ( x + 4 )        = 20 + 25

9 . ( x + 4 )        = 45

     ( x + 4 )       = 45 : 9

      x  + 4          = 5

      x                 = 5 - 4

      x                 = 1

3(x + 6) = 2(x - 5)

=> 3x + 18 = 2x - 10

=> 3x - 2x = -10 - 18

=> x = -28

vay_

c, |3x - 7| = 6

=> 3x - 7 = 6 hoac 3x - 7 = -6

=> 3x = 13 hoac 3x = 1

=> x = 13/3 hoac x = 1/3

vay_

3(x + 6) = 2(x - 5)

=> 3x + 18 = 2x - 10

=> 3x - 2x = -10 - 18

=> x = -28

Vậy x = -28

c, |3x - 7| = 6

=> 3x - 7 = 6 hoac 3x - 7 = - 6

=> 3x = 13 hoac 3x = 1

=> x = \(\frac{13}{3}\) hoac x = \(\frac{1}{3}\)

Vậy \(x\in\left\{\frac{3}{13};\frac{1}{3}\right\}\)

1) \(8x^3-12x^2+6x-1=0\)

\(\Leftrightarrow\left(2x\right)^2-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3=0\)

\(\Leftrightarrow\left(2x-1\right)^3=0\)

\(\Leftrightarrow2x-1=0\)

\(\Leftrightarrow2x=1\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

2) \(x^3-6x^2+12x-8=27\)

\(\Leftrightarrow x^3-3\cdot x^2\cdot2+3\cdot2^2\cdot x-2^3=27\)

\(\Leftrightarrow\left(x-2\right)^3=27\)

\(\Leftrightarrow\left(x-2\right)^3=3^3\)

\(\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=3+2\)

\(\Leftrightarrow x=5\)

3) \(x^2-8x+16=5\left(4-x\right)^3\)

\(\Leftrightarrow\left(x-4\right)^2=5\left(4-x\right)^3\)

\(\Leftrightarrow\left(4-x\right)^2=5\left(4-x\right)^3\)

\(\Leftrightarrow5\left(4-x\right)=1\)

\(\Leftrightarrow4-x=\dfrac{1}{5}\)

\(\Leftrightarrow x=4-\dfrac{1}{5}\)

\(\Leftrightarrow x=\dfrac{19}{5}\)

4) \(\left(2-x\right)^3=6x\left(x-2\right)\)

\(\Leftrightarrow8-12x+6x^2-x^3=6x^2-12x\)

\(\Leftrightarrow-12x+6x^2-6x^2+12x=8-x^3\)

\(\Leftrightarrow8-x^3=0\)

\(\Leftrightarrow x^3=8\)

\(\Leftrightarrow x^3=2^3\)

\(\Leftrightarrow x=2\)

5) \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-10\)

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-10\)

\(\Leftrightarrow\left(x^3-x^3\right)+\left(3x-3x\right)+\left(3x^2+3x^2\right)+\left(1+1\right)-6x^2+12x-6=-10\)

\(\Leftrightarrow0+0+0+\left(6x^2-6x^2\right)+12x-4=-10\)

\(\Leftrightarrow12x-4=-10\)

\(\Leftrightarrow12x=-10+4\)

\(\Leftrightarrow12x=-6\)

\(\Leftrightarrow x=\dfrac{-6}{12}\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

6) \(\left(3-x\right)^3-\left(x+3\right)^3=36x^2-54x\)

\(\Leftrightarrow27-27x+9x^2-x^3-x^3-9x^2-27x-27=36x^2-54x\)

\(\Leftrightarrow-54x-2x^3=36x^2-54x\)

\(\Leftrightarrow-2x^3=36x^2\)

\(\Leftrightarrow-2x^3-36x^2=0\)

\(\Leftrightarrow-2x^2\left(x+18\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-2x^2=0\\x+18=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-18\end{matrix}\right.\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{4}=\dfrac{y}{6}=\dfrac{z}{15}=\dfrac{x+3y-5z}{4+3\cdot6-5\cdot15}=\dfrac{-106}{-53}=2\)

Do đó: x=8; y=12; z=30

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

 5^x : 5² = 625

5^x : 5² = 5⁴

5^x  = 5^4. 5²

5^x  = 5⁶

^{\(\Rightarrow\)}x = 6

Vậy x =6

 5^x : 5² = 625

5^x-2=625

x-2=4

x=6

~~~~~~~~~~~~~Ai đi ngang qua nhớ để lại ti ck thanks~~~~~~~~~~~

5^x:5²=5^x-2=625=5³

^{\(\Rightarrow\)}x-2=3

          x=3+2

          x=5

\(3\left(x+6\right)=2\left(x-5\right)\)

\(\Rightarrow3.x+18=2x-10\)

\(\Rightarrow3x-2x=-10-18\)

\(\Rightarrow x=-28\)

\(\left|3.x-7\right|=6\)

\(\Leftrightarrow\orbr{\begin{cases}3x-7=6\\3x-7=-6\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3.x=13\\3x=1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{13}{3}\\x=\frac{1}{3}\end{cases}}\)

a)x.(x+1)<0 suy ra 2 số sẽ khác dấu.Ta xét 2 TH

TH1

x<0                                                             

x+1>0suy ra x>-1(loai)      

TH2

x>0                                     

x+1<0suy ra x<-1   mà x thuộc Z suy ra -1>x

Vậy x thuộc{-2;-3;...}