A,   \(4^{2x-6}=1\)

\(\Rightarrow4^{2x-6}=4^0\)

\(\Rightarrow2x-6=0\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=3\)

B,   \(5^{2x-3}-2.5^2=5^2.3\)

\(\Rightarrow5^{2x-3}=5^2.3+2.5^2\)

\(\Rightarrow5^{2x-3}=5^2.\left(3+2\right)\)

\(\Rightarrow5^{2x-3}=5^2.5\)

\(\Rightarrow5^{2x-3}=5^3\)

\(\Rightarrow2x-3=3\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=3\)

A, 4^2x-6=1

    4^2x-6=4⁰

    2x-6=0

    2x   =0+6

    2x   =6

    x     =3

B, 5^2x-3-2.5²=5².3

    5^2x-3         =5².3+2.5²

    5^2x-3           =5²(3+2)

    5^2x-3         =5³

     2x-3           =3

     x                = 3

\(4^{2x-6}=1\)

\(\Rightarrow4^{2x-6}=4^0\)

\(\Rightarrow2x-6=0\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=3\)

Bài 1 :

Gọi 3 số tự nhiên cần tìm là n - 1 ; n ; n + 1 ( với n \(\in\) N* )

Theo bài ra , ta có :

[ ( n -1 )n ] + [ ( n + 1 )n ] + [ (n - 1)( n + 1 ) ] = 242

=> ( \(n^2\) - n ) + ( \(n^2\) + n ) + ( \(n^2\) + n - n - 1 ) = 242

=> \(3n^2\) - 1 = 242

=> \(3n^2\) = 243

=> \(n^2\) = 81

=> n = 9 hoặc n = -9

Mà n là số tự nhiên \(\Rightarrow\) n = 9

Vậy 3 số cần tìm là 8 ; 9 ; 10

1) \(\left|2x+5\right|\ge21\Rightarrow2x+5\ge21\)hoặc \(2x+5

2b) Áp dụng bất đẳng thức giá trị tuyệt đối: |a| + |b|  \(\ge\) |a + b|. Dấu "=" xảy ra khi tích a.b \(\ge\) 0 

Ta có: B = |2x - 1| + |3 - 2x| + 5  \(\ge\) |2x - 1+3 - 2x| + 5  = |2| + 5 = 7

=> Min B = 7 khi

(2x - 1)( 3 - 2x) \(\ge\) 0 => (2x - 1)(2x - 3) \(\le\) 0 

Mà 2x - 1 > 2x - 3 nên 2x - 1 \(\ge\) 0 và 2x - 3 \(\le\)  0 

=> x \(\ge\) 1/2 và x  \(\le\) 3/2

1)

2x.(x-2) - x.(2x+1) = 3

=> 2x² - 4x - 2x² - x = 3

=> (2x² - 2x² ) - (4x+x) = 3

=> -5x = 3

=> x = \(\dfrac{-3}{5}\)

2) (2x-1).(x-2) - (x+3).(2x-7) = 3

=> 2x² - 4x - x + 2 - 2x² + 7x - 6x + 21 = 3

=> (2x² - 2x²) - (4x + 6x + x - 7x) + 2 + 21 = 3

=> -4x = -20

=> x = -20 : (-4)

=> x = 5

3) (x - 5).(-x + 4) - (x - 1).(x + 3) = -2x²

=> Bạn tách tương tự như mấy câu 2 nhé! Nếu không làm được thì bảo mình

\(a,\dfrac{3}{2}\cdot x-1=\dfrac{1}{2}x-\dfrac{3}{5}\)

\(\Rightarrow\dfrac{3}{2}x-\dfrac{1}{2}x=-\dfrac{3}{5}+1\)

\(\Rightarrow\left(\dfrac{3}{2}-\dfrac{1}{2}\right)x=-\dfrac{3}{5}+\dfrac{5}{5}\)

\(\Rightarrow x=\dfrac{2}{5}\)

\(b,\dfrac{1}{2}x+\dfrac{1}{2}\left(x-2\right)=\dfrac{3}{4}-2x\)

\(\Rightarrow\dfrac{1}{2}x+\dfrac{1}{2}x+2x-1=\dfrac{3}{4}\)

\(\Rightarrow\left(\dfrac{1}{2}+\dfrac{1}{2}+2\right)x=\dfrac{3}{4}+1\)

\(\Rightarrow3x=\dfrac{7}{4}\)

\(\Rightarrow x=\dfrac{7}{4}:3\)

\(\Rightarrow x=\dfrac{7}{12}\)

\(c,\left(x-\dfrac{1}{2}\right)-\dfrac{1}{4}=0\)

\(\Rightarrow x-\dfrac{1}{2}=\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{1}{4}+\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{4}+\dfrac{2}{4}\)

\(\Rightarrow x=\dfrac{3}{4}\)

\(d,4^{x-3}+1=17\)

\(\Rightarrow4^{x-3}=17-1\)

\(\Rightarrow4^{x-3}=16\)

\(\Rightarrow4^{x-3}=4^2\)

\(\Rightarrow x-3=2\)

\(\Rightarrow x=2+3\)

\(\Rightarrow x=5\)

#Toru

`3/2 x -1 =1/2x -3/5`

`=> 3/2x -1/2x = -3/5 +1`

`=> 2/2x= -3/5 + 5/5`

`=> x= 2/5`

__

`1/2x +1/2(x-2) = 3/4 -2x`

`=> 1/2x + 1/2x - 2/2 = 3/4 -2x`

`=> 1/2x +1/2x +2x = 3/4 + 1`

`=> 1/2x +1/2x + 4/2x = 3/4 +4/4`

`=> 6/2x = 7/4`

`=> x= 7/4 : 3`

`=>x=7/12`

__

`(x-1/2) -1/4=0`

`=> x-1/2=1/4`

`=> x=1/4 +1/2`

`=> x= 1/4 +2/4`

`=>x=3/4`

__

`4^(x-3) +1=17`

`=> 4^(x-3) =17-1`

`=> 4^(x-3)=16`

`=> 4^(x-3)=4^2`

`=> x-3=2`

`=>x=2+3`

`=>x=5`

a) \(5^4:\left(2x-1\right)^2=25\\ \Leftrightarrow5^4:\left(2x-1\right)^2=5^2\\ \Leftrightarrow5^4:5^2=\left(2x-1\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^2=5^2\\\left(2x-1\right)^2=\left(-5\right)^2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

b) \(17^3.x=17^4\\ \Rightarrow x=17^4:17^3=17\)

c) \(\left(2x+1\right)^3:49=7\\ \Leftrightarrow\left(2x-1\right)^3:7^2=7\\ \Leftrightarrow\left(2x-1\right)^3=7.7^2=7^3\\ \Leftrightarrow2x-1=7\\ \Leftrightarrow x=4\)

a)5⁴ : (2x - 1)² =25

5⁴ : (2x - 1)² =5²

(2x - 1)² =5⁴ : 5²

(2x - 1)² = 5²

2x - 1 = 5

2x = 5+1

2x = 6

x = 6: 2

x = 3

b)17³.x = 17⁴

x = 17⁴ : 17³

x = 17

c)(2x + 1)³ : 49 =7

(2x + 1)³ = 7 . 49

(2x + 1)³ = 343

(2x + 1)³ = 7³

2x +1 = 7

2x = 7- 1

2x = 6

x = 6:2

x = 3

a) 5⁴ : (2x - 1)² = 25

625 : (2x - 1)² = 25

(2x - 1)² = 625 : 25

(2x - 1)² = 25

(2x - 1)² = 5²

(2x - 1) = 5

2x = 5 + 1

2x = 6

x = 6 : 2

x = 3

b) 173 . x = 174

x = 17⁴ : 17³

x = 17¹

x = 17

c) (2x + 1)³ : 49 = 7

(2x + 1)³ = 7 . 49

(2x + 1)³ = 343

(2x + 1)³ = 7³

(2x + 1) = 7

2x = 7 - 1

2x = 6

x = 6 : 2

x = 3

\(\dfrac{2x-1}{x+1}=\dfrac{-2x+1}{x-5}\left(x\ne-1;5\right)\)

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

\(x+1=5-x\)

\(2x=4\Rightarrow x=2\)

bài 1

a)\(x^2+5x+6=\left(x+2\right)\left(x+3\right)=0\Leftrightarrow\orbr{\begin{cases}x+3=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=-2\end{cases}}}\)