\(8-36x+54x^2-27x^3=0\)

\(=2^3-3.2^2.3x+3.9x^2.2-3x^3\)

\(=2-3x^3=0\)

\(\Rightarrow2-3x=0\Rightarrow x=\frac{2}{3}\)

=2^3-3.2^2.3x+3.9x^2.2-(3x)^3

=(2-3x)^3=0

2-3x=0=>x=2/3

dung roi do 2 phan 3

a, A = 27x³ + 54x² + 36x + 4

=> A = (3x)³ + 2 . 3 . 9x² + 3 . 3x . 4 + 8 - 4

=> A = [(3x)³ + 2 . 3 . (3x)² + 3 . 3x . 2² + 2³] - 4

=> A = (3x + 2)³ - 4

Thay x = -2002 vào A ta có: A = (3x + 2)³ - 4 

=> A = [3 x (-2002) + 2]³ - 4 = [6006 + 2]³ - 4 = 6008³ - 4

b, B = 2x² + 4x + xy + 2y

=> B = 2x(x + 2) + y(x + 2)

=> B = (x + 2)(2x + y)

Thay x = 88; y = -76 vào B

=> B = (88 + 2)[2 . 88 + (-76)]

=> B = 90 . [176 + (-76)] = 90 . 100 = 9000

\(a,M=27x^3+108x^2+144x+64=\left(3x+4\right)^2\)Tại \(x=32\Rightarrow M=\left(3.32+4\right)^3=100^3=1000000\)

\(b,N=27x^3-54x^2+36x-8=\left(3x-2\right)^3\)

Tại \(x=14\Rightarrow N=\left(3.14-2\right)^3=40^3=64000\)

a)  \(49x^2-56x+16\) 

\(=\left(7x-4\right)^2\)

\(=\left(7.2-4\right)^2=100\)

b) mk chỉnh lại đề

  \(27x^3+54x^2+36x+8\)  

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

\(=\left[3.\left(-2\right)+2\right]^3=-64\)

c)  \(\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)+3\left(x+1\right)\left(x^2+x+1\right)+3\left(x-1\right)^2\)

\(=6x^2+7x+5\)

\(=6.\left(-\frac{2}{5}\right)^2+7.\left(-\frac{2}{5}\right)+5\)

\(=\frac{79}{25}\)

Bạn ơi có đúng không?

Bài 2: 

a: \(A=a^2+b^2+c^2+2ab-2ac-2bc+a^2+b^2+c^2-2ab-2bc+2ac\)

\(=2a^2+2b^2+2c^2-4bc\)

\(=2+2\cdot9+2\cdot1-4\cdot3\cdot\left(-1\right)=22+12=34\)

b: \(B=\left(a+b-a+b\right)\left(a+b+a-b\right)=4ab=4\cdot2\cdot5=40\)

(x - 5)² = (3 + 2x)²

(x - 5)² - (3 + 2x)² = 0

[(x - 5) - (3 + 2x)][(x - 5) + (3 + 2x)] = 0

(x - 5 - 3 - 2x)(x - 5 + 3 + 2x) = 0

(-x - 8)(3x - 2) = 0

-x - 8 = 0 hoặc 3x - 2 = 0

*) -x - 8 = 0

-x = 8

x = -8

*) 3x - 2 = 0

3x = 2

x = 2/3

Vậy x = -8; x = 2/3

--------------------

27x³ - 54x² + 36x = 9

27x³ - 54x² + 36x - 9 = 0

27x³ - 27x² - 27x² + 27x + 9x - 9 = 0

(27x³ - 27x²) - (27x² - 27x) + (9x - 9) = 0

27x²(x - 1) - 27x(x - 1) + 9(x - 1) = 0

(x - 1)(27x² - 27x + 9) = 0

x - 1 = 0 hoặc 27x² - 27x + 9 = 0

*) x - 1 = 0

x = 1

*) 27x² - 27x + 9 = 0

Ta có:

27x² - 27x + 9

= 27(x² - x + 1/3)

= 27(x² - 2.x.1/2 + 1/4 + 1/12)

= 27[(x - 1/2)² + 1/12] > 0 với mọi x ∈ R

⇒ 27x² - 27x + 9 = 0 (vô lí)

Vậy x = 1

A = x² + y²

= x² - 2xy + y² + 2xy

= (x - y)² + 2xy

= 4² + 2.1

= 16 + 2

= 18

B = x³ - y³

= (x - y)(x² + xy + y²)

= (x - y)(x² - 2xy + y² + xy + 2xy)

= (x - y)[(x - y)² + 3xy]

= 4.(4² + 3.1)

= 4.(16 + 3)

= 4.19

= 76

C = x⁴ + y⁴

= (x²)² + (y²)²

= (x²)² + 2x²y² + (y²)² - 2x²y²

= (x² + y²)² - 2x²y²

= (x² - 2x²y² + y² + 2x²y²)² - 2x²y²

= [(x - y)² + 2x²y²]² - 2x²y²

= (4² + 2.1²)² - 2.1²

= (16 + 2)² - 2

= 18² - 2

= 324 - 2

= 322

a: =>(2x+3)^2-(x-5)^2=0

=>(2x+3+x-5)(2x+3-x+5)=0

=>(x+8)(3x-2)=0

=>x=2/3 hoặc x=-8

b: =>27x^3-54x^2-36x-9=0

=>3x^3-6x^2-4x-1=0

=>\(x\simeq2,57\)

c: A=x^2+y^2=(x-y)^2+2xy=4^2+2=18

B=x^3-y^3=(x-y)^3+3xy(x-y)

=4^3+3*1*4

=64+12=76

C=(x^2+y^2)^2-2x^2y^2

=18^2-2*1^2=322

\(x^2+x+\dfrac{1}{4}=\left(x+\dfrac{1}{4}\right)^2\)

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

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