\(\left(x+2\right)^2=\left(2x-1\right)^2\\ \Leftrightarrow\left(x+2\right)^2-\left(2x-1\right)^2=0\\\Leftrightarrow\left[x+2-\left(2x-1\right)\right]\left[x+2+2x-1\right]=0\\ \Leftrightarrow\left(x+2-2x+1\right)\left(x+2+2x-1\right)=0\\ \Leftrightarrow\left(-x+3\right)\left(3x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}-x+3=0\\3x+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}-x=-3\\3x=-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{3}\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x+2=2x-1\\x+2=-\left(2x-1\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2x=-1-2\\x+2=-2x+1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x=-3\\x+2x=1-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\3x=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{3}\end{matrix}\right.\)

(x+2)2=(2x−1)2⇔(x+2)2−(2x−1)2=0⇔[x+2−(2x−1)][x+2+2x−1]=0⇔(x+2−2x+1)(x+2+2x−1)=0⇔(−x+3)(3x+1)=0⇔[−x+3=03x+1=0​⇔[−x=−33x=−1​
 

=) x = 3 hoặc -1/3.

Chúc bạn hok tốt

\(...\Rightarrow x^3-9x^2+27x-27-\left(x^3-27\right)+9\left(x^2+2x+1\right)=15\)

\(\Rightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15\)

\(\Rightarrow45x+9=15\Rightarrow45x=6\Rightarrow x=\dfrac{6}{45}=\dfrac{2}{15}\)

Nhanh nha các bạn giúp mình

Tính bằng cách hợp lí nếu có thể

A) 21 . 35 - 3 . 25

B)48 . (-21) + (-142) . (-24)

C)77 - 11 . (30+7

\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)

Đặt \(\left(1\right)=A\)

\(\Rightarrow A=1+5^2+...+5^{2x}\)

\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)

\(\Rightarrow24A=5^{2x+2}-1\)

\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)

Mà: \(A=\dfrac{25^6-1}{24}\)

\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)

\(\Rightarrow5^{2x+2}-1=5^{12}-1\)

\(\Rightarrow5^{2x+2}=5^{12}\)

\(\Rightarrow2x+2=12\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=\dfrac{10}{2}\)

\(\Rightarrow x=5\)

a=10 

b=-39

c=4

25+(15-x)=30                          43-(24-x)=20                       24+3(5-x)=27

      (15-x)=25+30=55                   (24-x)=43-20=23                  3(5-x)=27-24=3

            x =55-15=40                           x =24-23=1                      (5-x)=3:3=1

                                                                                                        x =5-1=4

Hok tốt!

@Kaito Kid

Mình cần các bạn giúp gấp.

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

3) 

a) 10 + 2x = 49 : 47

10 + 2x = 49/47

2x = 49/47 - 10

2x = -421/47

x = -421/47 : 2

x = -421/94

b) 70 - 5(x - 3) = 45

5(x - 3) = 70 - 45

5(x - 3) = 25

x - 3 = 25 : 5

x - 3 = 5

x = 5 + 3

x = 8

c) 4 + 95 : x = 143 : 142 - 23

4 + 95 : x = -3123/142

95 : x = -3123/142 - 4

95 : x = -3691/142

x = 95 : (-3691/142)

x = -13490/3691

Câu 1: 

a: =>-2x-x+17=34+x-25

=>-3x+17=x+9

=>-4x=-8

hay x=2

b: =>17x+16x+27=2x+43

=>33x+27=2x+43

=>31x=16

hay x=16/31

c: =>-2x-3x+51=34+2x-50

=>-5x+51=2x-16

=>-7x=-67

hay x=67/7

e: 3x-32>-5x+1

=>8x>33

hay x>33/8

a) ( -2x - 28 )⁵ = -32 = ( -2 )⁵

-2x - 28 = -2

-2x = ( -2 ) + 28 = 26

x = 26 : ( -2 ) = -13

b) ( 7x - 11 )³ = 1000 = 10³

7x - 11 = 10

7x = 10 + 11 = 21

x = 21 : 7 = 3

c) ( 3x - 15 )² - 6 = 75

( 3x - 15 )² = 75 + 6 = 81 = 9²

3x - 15 = 9

3x = 9 + 15 = 24

x = 24 : 3 = 8

a) \(5\left(x-7\right)=0\)

\(\Rightarrow x-7=0\)

\(\Rightarrow x=7\)

b) \(25\left(x-4\right)=0\)

\(\Rightarrow x-4=0\)

\(\Rightarrow x=4\)

c) \(\left(34-2x\right)\left(2x-6\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}34-2x=0\\2x-6=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=34\\2x=6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=17\\x=3\end{matrix}\right.\)

d) \(\left(2019-x\right)\left(3x-12\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2019-x=0\\3x-12=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2019\\3x=12\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2019\\x=\dfrac{12}{3}=4\end{matrix}\right.\)

e) \(57\left(9x-27\right)=0\)

\(\Rightarrow9x-27=0\)

\(\Rightarrow9\left(x-3\right)=0\)

\(\Rightarrow x-3=0\)

\(\Rightarrow x=3\)

a) 5.(x-7)=0⇔x-7=0⇔x=7

b) 25(x-4)=0⇔x-4=0⇔x=4

c) (34-2x).(2x-6)=0

⇔ 34-2x=0 hoặc 2x-6=0

⇔2x=34 hoặc 2x=6

⇔ x=17 hoặc x=3

d) (2019-x).(3x-12)=0

⇔ 2019-x=0 hoặc 3x-12=0

⇔ x=2019 hoặc x=4

e) 57.(9x-27)=0

⇔ 9x-27=0

⇔ x=3

f) 25+(15-x)=30

⇔ 15-x=5

⇔ x=10

g) 43-(24-x)=20

⇔ 24-x=23

⇔ x=1

h) 2.(x-5)-17=25

⇔ 2(x-5)=42

⇔x-5=21

⇔ x=26

i) 3(x+7)-15=27

⇔ 3(x+7)=42

⇔ x+7=14

⇔ x=7

j) 15+4(x-2)=95

⇔ 4(x-2)=80

⇔ x-2=20

⇔ x=22

k) 20-(x+14)=5

⇔ x+14=15

⇔ x=1

l) 14+3(5-x)=27

⇔ 3(5-x)=13

⇔ 5-x=13/3

⇔ x=5-13/3

⇔ x=2/3