\(5^{2x-3}-25^2=5^{2.3}\)

\(5^{2x-3}-\left(5^2\right)^2=5^6\)

\(5^{2x-3}-5^4=5^6\)

-> 2x - 3 - 4 = 6

2x - 3 = 4 + 6

2x - 3 = 10

2x = 10 + 3

2x = 13

x = \(\frac{13}{2}\)

\(\frac{13}{2}=6,5\)nha

\(5^{2x}-3-25^2=3.5^2\)

\(25^x-25^2=3\left(5^2+1\right)\)

\(\Leftrightarrow25^x=78\)

Vậy........

gúp minh với ạ 

\(25^x+5^{2x+1}=150\)

\(5^{2x}+5^{2x}\cdot5=150\)

\(5^{2x}\cdot\left(1+5\right)=150\)

\(5^{2x}=25\)

\(5^{2x}=5^2\)

\(2x=2\)

\(x=1\)

( 3x - 1 )^2 = 25 = (+-5)^2

+) 3x - 1 = 5

3x = 6

x = 2

+) 3x - 1 = -5

3x = -4

x = -4/3

Vậy,.........

Các câu còn lại tương tự

1.(x -5)^2 - 25 =0

=> (x - 5)^2 = 25

=> x - 5 = 5 hoặc x - 5 = -5

=> x = 10 hoặc x = 0

vậy_

2. (x -2)^3 =27

=> x - 2 = 3

=> x = 5

vậy_

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

=> 3x - 21 + 2x^2 + 4x = 2x^2

=> 7x - 21 = 0

=> 7x = 21

=> x = 3

vậy_

4. (x^2 - 4) (x +8) =0

=> x^2 - 4 = 0 hoặc x + 8 = 0

=> x^2 = 4 hoặc x = -8

=> x = 2 hoặc x = -2 hoặc x = -8

vậy_

5. x^ 2 + 3x = 0

=> x(x + 3) = 0 

=> x = 0 hoặc x + 3 = 0

=> x = 0 hoặc x = -3

vậy_

6. 3x^3 - 3x = 0

=> 3x(x^2 - 1) = 0

=> 3x(x - 1)(x + 1) = 0

=> x = 0 hoặc x = 1 hoặc x = -1

vậy_

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

=> (x + 1 + 2x + 3)(x + 1 - 2x - 3) = 0

=> (3x + 3)(-x - 2) = 0

=> x = -1 hoặc x = -2

vậy_

Bài làm

1) ( x - 5 )² - 25 = 0

<=> ( x - 5 - 5 )( x - 5 + 5 ) = 0

<=> x( x - 10 ) = 

<=> \(\orbr{\begin{cases}x=0\\x-10=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=10\end{cases}}}\)

Vậy S = { 0; 10 }

2) \(\left(x-2\right)^3=27\)

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

\(\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=5\)

Vậy x = 5 là nghiệm phương trình.

3) \(3\left(x-7\right)+2x\left(x+2\right)=2x^2\)

\(\Leftrightarrow3x+2x^2+4x-2x^2=21\)

\(\Leftrightarrow7x=21\)

\(\Leftrightarrow x=\frac{21}{7}=3\)

Vậy x = 3 là nghiệm phương trình

4) \(\left(x^2-4\right)\left(x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2-4=0\\x+8=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x^2=\pm2\\x=-8\end{cases}}}\)

Vậy S = { 2; -2; -8 }

5) \(x^2+3x=0\)

\(\Leftrightarrow x\left(x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-3\end{cases}}}\)

Vậy S = { 0; -3 } 

6) \(3x^3-3x=0\)

\(\Leftrightarrow3x\left(x^2-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x=0\\x^2-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}}\)

Vậy S = { +1; 0 }

7) \(\left(x+1\right)^2=\left(2x+3\right)^2\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}-x-2=0\\3x+4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-\frac{4}{3}\end{cases}}}\)

Vậy S = { -2; -4/3 }

# Học tốt #

a)

\(\text{( 25 – 2x )³ : 5 – 3^2 = 4^2}\)

\(\text{( 25 – 2x )³ : 5 – 9 = 16}\)

\(\text{( 25 – 2x )³ : 5 = 16 + 9}\)

\(\text{( 25 – 2x )³ : 5 = 25}\)

\(\text{( 25 – 2x )³ = 25 . 5}\)

\(\text{( 25 – 2x )³ = 125}\)

\(\text{( 25 – 2x )³ = 5³}\)

\(\text{25 – 2x = 5}\)

\(\text{2x = 25 – 5}\)

\(\text{2x = 20}\)

\(\text{x = 10}\)

\(\text{________________________________________}\)

b)

\(\text{2.3^x = 10.3^12 + 8.27^4}\)

\(\text{2.3^x = 10.3^12 + 8.(3^3)^4}\)

\(\text{2.3^x = 3^12 . (10+8)}\)

\(\text{2.3^x = 3^12 . 18}\)

\(\text{3^x = 3^12 . 18:2}\)

\(\text{3^x = 3^12 . 9}\)

\(\text{3^x = 3^12 . 3^2}\)

\(\text{3^x = 3^14}\)

\(\text{=> x=14}\)

Bài 2: 

a: \(\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x+5\right)=0\)

=>(x+5)(x-6)=0

=>x=-5 hoặc x=6

b: \(\Leftrightarrow4x^2-4x+1-4x^2+1=0\)

=>-4x+2=0

hay x=1/2

c: \(\Leftrightarrow\left(x^2+4\right)\left(x^2-1\right)=0\)

=>x=1 hoặc x=-1

\(\left(x+1\right)^3=27\)

\(\left(x+1\right)^3=3^3\)

\(\Rightarrow x+1=3\)

\(x=2\)

\(\left(x+1\right)^3=27\)

\(< =>\left(x+1\right)^3=3.3.3=3^3\)

\(< =>x+1=3< =>x=3-1=2\)

\(\left(2x+3\right)^3=9.81\)

\(< =>\left(2x+3\right)^3=9.9.9\)

\(< =>\left(2x+3\right)^3=9^3\)

\(< =>2x+3=9< =>2x=6\)

\(< =>x=\frac{6}{2}=3\)

giúp mình bài này đi

21.73 + 27 . 21

b, x = -5/3 hoặc x = 4/3.

c, x = 0 hoặc x = 3, -3.

d, x = 0 hoặc x = 2, -2.

e, x = 1 hoặc x = \(\dfrac{-1}{2}\).

a: \(\Leftrightarrow x^2-40x+400-x^2-4x-3=-7\)

=>-44x+397=-7

=>-44x=-404

hay x=101

b: \(\Leftrightarrow\left[{}\begin{matrix}3x+5=0\\4-3x=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{5}{3};\dfrac{4}{3}\right\}\)

c: \(\Leftrightarrow x\left(x^2-9\right)=0\)

=>x(x-3)(x+3)=0

hay \(x\in\left\{0;3;-3\right\}\)

d: \(\Leftrightarrow x\left(x-2\right)\left(x+2\right)=0\)

hay \(x\in\left\{0;2;-2\right\}\)

e: =>(2x+1)(1-x)=0

=>x=-1/2 hoặc x=1