\(A=3^x+3^{x+1}+...+3^{x+100}\)

=>\(3A=3^{x+1}+3^{x+2}+...+3^{x+101}\)

=>\(2A=3^{x+101}-3^x\)

=>\(A=\dfrac{3^{x+101}-3^x}{2}\)

=>\(3^{x+101}-3^x=3^{105}-3^4\)

=>x=4

x=4

( 3. x + 1 )3 = 343

( 3. x + 1 )3 = 73

=> 3x + 1 = 7

=> 3x = 6

=> x = 2

\(\left(3x+1\right)^3=243\\ \left(3x+1\right)^3=7^3\\ 3x+1=7\\ 3x=6\\ x=2\)

a ) ( x - 1 )³ = 343

7³ = 343

x + 1 = 7

x = 7 - 1

x = 6

b ) ( x - 2 )⁴ = 4096

8⁴ = 4096

x - 2 = 8

x = 8 + 2

x = 10

\(\left(x-1\right)^3=343=7^3\) => x -1 =7 => x =8

\(\left(x-2\right)^4=4096=8^4=\left(-8\right)^4\)\(\Rightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}\Rightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)

a) \(\left(x-1\right)^3=343\)

\(\left(x-1\right)=7^3\)

  \(x-1=7\)

  \(x=7+1\)        

  \(x=8\)

b) \(\left(x-2\right)^4=4094\)

    \(\left(x-2\right)^4=8^4\)

      \(x-2=8\) hoặc \(x-2=-8\)

      \(x=8+2\)         \(x=-8+2\)

      \(x=10\)               \(x=-6\)

Vậy \(x=10\) hoặc \(x=-6\)

=>(x+1)³=7³

=>x+1=7

=>x=6

(x+1)^3=-343

x+1     = -7

x      =-7-1

x       =-8

tick nha Ngô Nhất Khánh yêu quý

\(\left(2x+1\right)^3=343\)

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

\(\Rightarrow2x+1=7\)

\(2x=7-1\)

\(2x=6\)

\(x=6:2\)

\(x=3\)

Vậy x = 3

Ta có: (2x + 1)³ = 343

     \(\Leftrightarrow\)(2x + 1)³ = 7³

    \(\Leftrightarrow\)2x + 1 = 7

    \(\Leftrightarrow\)2x = 7 - 1 = 6

    \(\Leftrightarrow\)x = 6: 2 = 3

Vay x = 3

ta có 

(2x+1)^3=343

<=>(2x+1)^3=7^3

=>2x+1=7

=>x=4

Ai đó hãy giúp giải bà này đi 

Chọn A

\(\left(2x+1\right)^3=343\)

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

\(\Rightarrow2x+1=7\)

\(\Rightarrow2x=7-1\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=6:2\)

\(\Rightarrow x=3\)

Vậy x = 3

_Chúc bạn học tốt_

\(\left(2x+1\right)^3=343\)

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

\(2x+1=7\)

\(2x=7-1\)

\(2x=6\)

\(x=6:2\)

\(x=3\)

\(x^3=343\)

hay x=7