a) \(\left(3x-2\right)\left(9x^2+6x+4\right)-\left(3x-1\right)\left(9x^2-3x+1\right)=x-4\)

\(\Leftrightarrow\left(3x-2\right)\left[\left(3x\right)^2+3x\cdot2+2^2\right]-\left(3x-1\right)\left[\left(3x\right)^2+3x\cdot1+1\right]=x-4\)

\(\Leftrightarrow\left(3x\right)^3-2^3-\left[\left(3x\right)^3-1\right]=x-4\)

\(\Leftrightarrow x=-3\) ( thỏa mãn )

P/s : Đề câu b) viết lại nhé, mình không hiểu lắm :))

\(9\left(2x+1\right)=4\left(x-5\right)^2\)

\(\Leftrightarrow18x+9=4\left(x^2-10x+25\right)\)

\(\Leftrightarrow18x+9=4x^2-40x+100\)

\(\Leftrightarrow4x^2-58x+91=0\)

Ta có \(\Delta=58^2-4.4.91=1908,\sqrt{\Delta}=6\sqrt{53}\)

\(\Rightarrow x=\frac{58\pm6\sqrt{53}}{8}\)

a) Ta có: \(A=\left(4-x\right)\left(16+4x+x^2\right)-\left(4-x\right)^3\)

\(=64-x^3+\left(x-4\right)^3\)

\(=64-x^3+x^3-12x^2+48x-64\)

\(=-12x^2+48x\)

b) Ta có: \(B=\left(3x+2\right)\left(9x^2-6x+4\right)-\left(3x-2\right)\left(9x^2+6x+4\right)\)

\(=27x^3+8-27x^3+8\)

=16

c) Ta có: \(C=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)^2\)

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

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

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

\(M=3\left(3x+1\right)\left(9x^2-3x+1\right)-\left(x^3+1\right)\)

\(=3\left(27x^3+1\right)-x^3-1=80x^3+2=80.\left(\dfrac{1}{2}\right)^3+2=12\)

Sửa đề: \(N=\left(3x+1\right)\left(9x^2-3x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)

\(N=27x^3+1-x^3-1=26x^3=26.10^3=26000\)

2:

a: \(9x^2-1=\left(3x\right)^2-1=\left(3x-1\right)\left(3x+1\right)\)

b: \(2\left(x-1\right)+x^2-x\)

\(=2\left(x-1\right)+x\left(x-1\right)\)

\(=\left(x-1\right)\left(x+2\right)\)

c: \(3x^2+14x-5\)

\(=3x^2+15x-x-5\)

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

3: 

a: \(2x\left(x-1\right)-2x^2=4\)

=>\(2x^2-2x-2x^2=4\)

=>-2x=4

=>x=-2

b: \(x\left(x-3\right)-\left(x+2\right)\left(x-1\right)=5\)

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

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

=>-4x=3

=>x=-3/4

c: \(4x^2-25+\left(2x+5\right)^2=0\)

=>\(\left(2x-5\right)\left(2x+5\right)+\left(2x+5\right)^2=0\)

=>\(\left(2x+5\right)\left(2x-5+2x+5\right)=0\)

=>4x(2x+5)=0

=>\(\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\end{matrix}\right.\)

\(1,=x^6+27\\ 2,=8x^3+1\\ 3,=x^6+8\\ 4,=27x^3+8\)

1. (x² + 3)(x⁴ - 3x² + 9)

= x⁶ + 27

2. (2x + 1)(4x² - 2x + 1)

= 8x³ + 1

3. (x² + 2)(x⁴ - 2x² + 4)

= x⁶ + 8

4. (3x + 2)(9x² - 6x + 4)

= 27x³ + 8

1: \(\left(x^2+3\right)\left(x^4-3x^2+9\right)=x^6+27\)

2: \(\left(2x+1\right)\left(4x^2-2x+1\right)=8x^3+1\)

3: \(\left(x^2+2\right)\left(x^4-2x^2+4\right)=x^6+8\)

4: \(\left(3x+2\right)\left(9x^2-6x+4\right)=27x^3+8\)

b: \(\Leftrightarrow9x^2+12x+4-18x+12=9x^2\)

=>-6x+16=0

=>-6x=-16

hay x=8/3(nhận)

c: \(\Leftrightarrow\dfrac{x+1+x-1}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x+2}\)

\(\Leftrightarrow2x\left(x+2\right)=2\left(x^2-1\right)\)

\(\Leftrightarrow2x^2+4x-2x^2+2=0\)

=>4x+2=0

hay x=-1/2(nhận)

a. 9x² - 6x - 3 = 0

<=> 3(3x² - 2x - 1) = 0

<=> 3(3x² - 3x + x - 1) = 0

<=> \(3\left[3x\left(x-1\right)+\left(x-1\right)\right]=0\)

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

<=> \(\left[{}\begin{matrix}3x+1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=1\end{matrix}\right.\)

b. (2x + 1)² - 4(x + 2)² = 9

<=> (2x + 1)² - \(\left[2\left(x+2\right)\right]^2=9\)

<=> (2x + 1 - 2x - 4)(2x + 1 + 2x + 4) = 9

<=> -3(4x + 5) = 9

<=> 4x + 5 = -3

<=> 5 + 3 = -4x

<=> -4x = 8

<=> -x = 2

<=> x = -2

a) \(\Leftrightarrow\left(9x^2-6x+1\right)-4=0\)

\(\Leftrightarrow\left(3x-1\right)^2-4=0\)

\(\Leftrightarrow3\left(x-1\right)\left(3x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)

b) \(\Leftrightarrow4x^2+4x+1-4x^2-16x-16=9\)

\(\Leftrightarrow12x=-24\Leftrightarrow x=-2\)

c) \(\Leftrightarrow3x^2-6x+3-3x^2+15x=21\)

\(\Leftrightarrow9x=18\Leftrightarrow x=2\)

d) \(\Leftrightarrow x^2+6x+9-x^2-4x+32=1\)

\(\Leftrightarrow2x=-40\Leftrightarrow x=-20\)

c: \(x^2+4x+4=\left(x+2\right)^2\)

d: \(9x^2+6x+1=\left(3x+1\right)^2\)

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

​​Giải pt : 

(3x-2)(9x2+6x+4)-(3x-1)(9x2-3x+1)=x-4

9(2x+1)=4(x-5)2

\(9\left(2x+1\right)=4\left(x-5\right)2\)

\(18x+9=4x-40\)

\(18x-4x=-40-9\)

\(14x=-49\)

\(x=-\frac{7}{2}\)

(3x - 2)(9x² + 6x + 4) - (3x - 1)(9x² - 3x + 1) = x - 4

<=> 27x³ - 8 - 27x³ + 1 = x - 4

<=> x - 4 = -7

<=> x=  -3

Vậy S = {-3}

9(2x + 1) = 4(x - 5)²

<=> 18x + 9 - 4x² + 40x - 100 = 0

<=> -4x² + 58x - 91 = 0

<=> -(4x² - 58x + 210,25 - 119,25) = 0

<=> (2x - 14,5)² = 119,25

<=> \(\orbr{\begin{cases}2x-14,5=\sqrt{119,25}\\2x-14,5=-\sqrt{119,25}\end{cases}}\)

<=> \(\orbr{\begin{cases}x=\frac{29+3\sqrt{53}}{4}\\x=\frac{29-3\sqrt{53}}{4}\end{cases}}\)

Vậy S = {...}