Đặt A = 1 + 3 + 3² + ... + 3¹¹

3A = 3 + 3² + 3³ + ... + 3¹²

3A - A = ( 3 + 3² + 3³ + ... + 3¹² ) - ( 1 + 3 + 3² + ... + 3¹¹ )

2A = 3¹² - 1

A = \(\dfrac{3^{12}-1}{2}\)

\(7.3^x+20.3^x=3^{25}\)

\(\Leftrightarrow3^x.27=3^{25}\)

\(\Leftrightarrow3^x=3^{25}:3^3\)

\(\Leftrightarrow x=22\)

( 7 + 20 ) .3^x = 3²⁵

27 . 3^x = 3²⁵ 

3³ . 3^x = 3²⁵

      3^x = 3²⁵ : 3³ 

      3^x = 3^25-3

      3^x = 3²²

=> x = 22

vậy x = 22

 8 + ( x - 9 ) = 125 - 64

8 + ( x - 9 ) = 61

x - 9 = 61 - 8

x - 9 = 53

x = 53 + 9

x = 62

vậy x = 62

\(2^3+x+3^2=5^3-4^3\)

\(\Leftrightarrow8+x+3^2=61\)

\(\Leftrightarrow x+3^2=53\)

\(\Leftrightarrow x=44\)

19 x 25 + 19 x 16 + 41

= 19 x (25 + 16) + 41

= 19 x 41 + 41

= (19 + 1) x 41

= 20 x 41

= 820

\(19\times25+19\times16+41\)

\(=19\times\left(25+16\right)+41\)

\(=41\times20=820\)

A = 8² : 4 . 3 + 2.5^2

A =  64 :4 .3 + 10.5

A = 16 .3 +50

A = 48 + 50

A = 98

= 64 : 4 . 3 + 2 . 25

= 16 . 3 + 50

= 48 + 50

= 98

x.(2x-1).(3x-126)=0

\(\Rightarrow\left[{}\begin{matrix}x=0\\2x-1=0\\3x-126=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\3x=126\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=42\end{matrix}\right.\)

X.(2X  - 1) .(3X - 126) = 0

X = 0 ;

2x- 1 =0  ⇒ x = 1/2

3x - 126 = 0

 x = 126: 3

x = 42

\(A=2+2^2+2^3+.....+2^{2023}+2^{2024}+2^{2025}\)

\(A=2\left(1+2+4\right)+.....+2^{2023}\left(2+2+4\right)\)

\(A=2.7+.....+2^{2023}.7⋮7\left(đpcm\right)\)

\(A=2+2^2+2^3+...+2^{2025}\\ A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{2023}+2^{2024}+2^{2025}\right)\\ A=2.\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{2023}\left(1+2+2^2\right)\\ A=2.7+2^4.7+2^7.7+...+2^{2023}.7\\ A=\left(2+2^4+2^7+...+2^{2023}\right).7⋮7\)

Vậy \(A⋮7\left(đpcm\right)\)

đề bài là gì vậy bn

\(A=2+2^2+2^3+....+2^{2024}+2^{2025}\)

\(\Leftrightarrow2A=2^2+2^3+2^4+....+2^{2025}+2^{2026}\)

\(\Leftrightarrow2A-A=A=2^{2026}-2\)

\(3\left(x+30\right)=8\)

\(\Leftrightarrow x+30=\dfrac{8}{3}\)

\(\Leftrightarrow x=\dfrac{-82}{3}\)

6, 28,  46, 47, 48, 

99