(3.x)^2 : 3^3=243

9.x^2 : 27=243

9.x^2=243.27

9.x^2=6561

x^2=6561:9

x^2=729

X=27

\(\left(x+3\right)^3-3\cdot\left(3x+1\right)^2+\left(2x+1\right)\cdot\left(4x^2-2x+1\right)=54\)

\(\Leftrightarrow x^3+9x^2+27x+27-3\cdot\left(9x^2+6x+1\right)+8x^3-4x^2+2x+4x^2-2x+1=54\)

\(\Leftrightarrow x^3+9x^2+27x+27-27x^2-18x-3+8x^3-4x^2+2x+4x^2-2x+1=54\)

\(\Leftrightarrow9x^3-18x^2+9x-29=0\)

\(\Leftrightarrow x=2,208024627\)

 (4x⁴+3x³):(-x³)+x.(15x²+6x):3x=0 (đk:x ≠ 0)

Vì x ≠ 0 nên ta rút gọn -x^3 và 3x cho cả tử và mẫu

PT <=> -4x-3+5x^2+2=0

       <=> 5x^2-2x-3=0

          <=> (x-1)(5x+3)=0

       <=> x=1 hoặc x=-5/3 (thỏa mãn)

Vậy x=1 hoặc x=-5/3 là nghiệm pt

a) \(3x\left(12x-4\right)-9x\left(4x-3\right)=30\)

\(\Rightarrow36x^2-12x-36x^2+27x=30\)

\(\Rightarrow\left(36x^2-36x^2\right)+\left(-12+27\right)=30\)

\(\Rightarrow0+15x=30\Leftrightarrow x=30:15=2\)

b) \(x\left(5-2x\right)+2x\left(x-1\right)=15\)

\(\Rightarrow5x-2x^2+2x^2-2x=15\)

\(\Rightarrow\left(5x-2x\right)+\left(-2x^2+2x^2\right)=15\)

\(\Rightarrow3x+0=15\Leftrightarrow x=15:3=5\)

a, 3x(12x - 4) - 9x(4x-3) = 30

36x² - 12x - 36x² + 27x = 30

- 12x + 27x = 30

15x = 30

x = 2

b, x(5 - 2x) + 2x(x - 1) = 15

5x - 2x² + 2x² - 2x = 15

5x - 2x = 15

3x = 15

x = 5

1a) -3x²(2x³ - 2x + 1/3) = -6x⁵ + 6x³ - x²

b) (x⁴ + 2x³ - 2/3).(-3x⁴) = -3x⁸ - 6x⁷ + 2x⁴

c) (x + 3)(x - 4) = x² - 4x + 3x - 12 = x² - x - 12

d)(x - 4)(x² + 4x + 16) = (x - 4)(x² + 4x + 4²) = x³ - 64

e) 4(x - 1/2)(x + 1/2)(4x² + 1) =4(x² - 1/4)(4x²  + 1) = 4(4x⁴ + x² - x² - 1/4) = 4(4x⁴ - 1/4) = 16x⁴ - 1

B2. a) (2 - x)(x² + 2x + 4) + x(x - 3)(x + 4) - x² + 24 = 0

=> 8 - x³ + x(x² + 4x - 3x - 12) - x² + 24 = 0

=> 8 - x³ + x³ + x² - 12x - x² + 24 = 0

=> -12x + 32 = 0

=> -12x = -32

=> x = -32 : (-12) = 8/3

b) (x/2 + 3)(5 - 6x) + (12x - 2)(x/4 + 3) = 0

=> 5x/2 - 3x² + 15 - 18x + 3x² + 36x - x/2 - 6 = 0

=> 20x + 9 = 0

=> 20x = -9

=> x = -9/20

\(\left(x-1\right).3+3x\left(x-4\right)+1=0\)

\(\Rightarrow3x-3+3x^2-12x+1=0\)

\(\Rightarrow3x^2-9x-2=0\)

\(\Rightarrow3\left(x^2-\frac{2.3}{2}.x+\frac{9}{4}\right)-\frac{35}{4}=0\)

\(\Rightarrow3\left(x-\frac{3}{2}\right)^2=\frac{35}{4}\Rightarrow\left(x-\frac{3}{2}\right)^2=\frac{35}{12}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{3}{2}=\sqrt{\frac{35}{12}}\\x-\frac{3}{2}=-\sqrt{\frac{35}{12}}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\sqrt{\frac{35}{12}}+\frac{3}{2}\\x=\frac{3}{2}-\sqrt{\frac{35}{12}}\end{cases}}\)

Vậy.....................