2.(1 + 3 + 3² + ... + 3ˣ) + 1 = 81

2.(3ˣ⁺¹ - 1)/2 + 1 = 81

3ˣ⁺¹ - 1 + 1 = 81

3ˣ⁺¹ = 81 

3ˣ⁺¹ = 3⁴

x + 1 = 4

x = 4 - 1

x = 3

Bài làm

a) 3x : 9 = 3⁹¹ 

=> 3x : 3² = 3⁹¹ 

=> 3x        = 3⁹¹ x 3² 

=> 3x        = 3⁹³ 

=>   x        = 3⁹³ : 3

=>   x        = 3⁹² 

Vậy x = 3⁹² 

b) 81 : 3x + 1 = 9

    81 : 3x       = 9 - 1

    81 : 3x       = 8

           3x       = 81 : 8

           3x       = 10,125

             x       = 10,125 : 3

             x       = 3,375

Vậy x = 3,375

# Học tốt #

a ) \(3x:9=3^{91}\)

\(\Rightarrow3x:3^2=3^{91}\)

\(3x=3^{91}.3^2\)

\(3x=3^{93}\)

\(x=3^{93}:3\)

\(x=3^{92}\)

Vậy \(x=3^{92}\)

b ) \(81:3x+1=9\)

        \(27x+1=9\)

         \(27.x=9-1\)

          \(27.x=8\)

              \(x=8:27\)

                  \(x=\frac{8}{27}\)

    Vậy \(x=\frac{8}{27}\)

        Chúc bạn học tốt !!!

3x:9=3⁹¹                         81:3x+1=9

3x:3²=3⁹¹                         3x+1=81:9

3x=3⁹¹.3²                         3x+1=9

3x=3⁹³                                   3x=10

  x=3⁹²                                x=10/3

vậy x=3⁹²                                 vậy x=10/3

                        (12x - 5)(4x + 3) + (3x - 5)(1 - 16x) = 81

⇔ 48x² + 36x - 20x - 15 + 3x - 48x² - 5 + 80x - 81 = 0

⇔                                                            99x - 101 = 0

⇔                                                                         x = \(\dfrac{101}{99}\)

\(\left(12x-5\right)\left(4x+3\right)+\left(3x-5\right)\left(1-16x\right)=81\)

\(\Leftrightarrow48x^2+36x-20x-15+3x-48x^2-5+80x=81\)

\(\Leftrightarrow99x=101\)

hay \(x=\dfrac{101}{99}\)

\(\left(\frac{-3}{4}\right)^{3x+5}=\left(\frac{81}{256}\right)^{-1}\)

\(\Rightarrow\left(\frac{-3}{4}\right)^{3x+5}=\frac{256}{81}\)

\(\Rightarrow\left(\frac{-3}{4}\right)^{3x+5}=\left(\frac{-3}{4}\right)^{-4}\)

\(\Rightarrow3x+5=-4\)

\(\Rightarrow3x=-9\)

\(\Rightarrow x=-3\)

Vậy x= -3

a/ \(\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)=81\)

<=> \(48x^2-12x-20x+5+3x-48x^2-7+112x=81\)

<=> \(83x-2=81\)

<=> \(83x=83\)

<=> \(x=1\)

b/ \(\left(2x-3\right)\left(2x+3\right)-\left(4x+1\right)x=1\)

<=> \(4x^2-9-4x^2-x=1\)

<=> \(-\left(9+x\right)=1\)

<=> \(9+x=-1\)

<=> \(x=-10\)

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

<=> \(3x^2-\left(3x^2-x+6x-2\right)=-7\)

<=> \(3x^2-3x^2+x-6x+2=-7\)

<=> \(-5x+2=-7\)

<=> \(-5x=-9\)

<=> \(x=\frac{9}{5}\)

mk chỉ phân tích thôi bạn tự chia nha!
a, \(16x^4-81=(4x^2)^2-9^2=(4x^2-9)(4x^2+9)\)

                    \(=[(2x)^2-3^2](4x^2+9)\)

                    \(=(2x+3)(2x-3)(4x^2+9)\)

b, \(x^3-3x^2+3x-1=(x-1)^3\)

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

c, \(18x^5+9x^4+3x^3+6x^2+3x+1=(18x^5+9x^4+3x^3)+(6x^2+3x+1)\)

\(=(6x^2+3x+1)(3x^3+1)\)

câu c bạn đánh sai 1 dấu phép toán kìa!!!!

Vũ Hồng Linh bạn check lại bài đầu dùm =_=" 

\(\left[-\frac{1}{3}\right]^3\cdot x=\frac{1}{81}\)

\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{3}\right]^3\)

\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{27}\right]\)

\(\Leftrightarrow x=\frac{1}{81}\cdot(-27)=-\frac{1}{3}\)

\(\left[x-\frac{1}{2}\right]^3=\frac{1}{27}\)

\(\Leftrightarrow\left[x-\frac{1}{2}\right]^3=\left[\frac{1}{3}\right]^3\)

=> Làm nốt 

Mấy bài kia cũng làm tương tự

a,

\(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

\(\dfrac{1}{4}:x=\dfrac{2}{5}-\dfrac{3}{4}\\ \)

\(\dfrac{1}{4}:x=\dfrac{8-15}{20}\)

\(\dfrac{1}{4}:x=\dfrac{-7}{20}\)

x = \(\dfrac{1}{4}:\dfrac{-7}{20}\)

\(x=\dfrac{-5}{7}\)

b,

( 3x + 1)^3 = 64

(3x + 1)^3 = 4^3

(3x + 1) = 4

3x = 4 - 1

3x = 3

x = 3 : 3

x = 1

c,

( 2x - 3)^4 = 81

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

(2x - 3) = 3

2x = 3 + 3

2x = 6

x = 6: 2

x = 3