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1.

\(x^4-6x^2-12x-8=0\)

\(\Leftrightarrow x^4-2x^2+1-4x^2-12x-9=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x^2-1=2x+3\\x^2-1=-2x-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-4=0\\x^2+2x+2=0\end{matrix}\right.\)

\(\Leftrightarrow x=1\pm\sqrt{5}\)

3.

ĐK: \(x\ge-9\)

\(x^4-x^3-8x^2+9x-9+\left(x^2-x+1\right)\sqrt{x+9}=0\)

\(\Leftrightarrow\left(x^2-x+1\right)\left(\sqrt{x+9}+x^2-9\right)=0\)

\(\Leftrightarrow\sqrt{x+9}+x^2-9=0\left(1\right)\)

Đặt \(\sqrt{x+9}=t\left(t\ge0\right)\Rightarrow9=t^2-x\)

\(\left(1\right)\Leftrightarrow t+x^2+x-t^2=0\)

\(\Leftrightarrow\left(x+t\right)\left(x-t+1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-\sqrt{x+9}\\x=\sqrt{x+9}-1\end{matrix}\right.\)

\(\Leftrightarrow...\)

2.

ĐK: \(x\ne\dfrac{2\pm\sqrt{2}}{2};x\ne\dfrac{-2\pm\sqrt{2}}{2}\)

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

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

Đặt \(2x+\dfrac{1}{x}+4=a;2x+\dfrac{1}{x}-4=b\left(a,b\ne0\right)\)

\(pt\Leftrightarrow\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{3}{5}\left(1\right)\)

Lại có \(a-b=8\Rightarrow a=b+8\), khi đó:

\(\left(1\right)\Leftrightarrow\dfrac{1}{b+8}+\dfrac{1}{b}=\dfrac{3}{5}\)

\(\Leftrightarrow\dfrac{2b+8}{\left(b+8\right)b}=\dfrac{3}{5}\)

\(\Leftrightarrow10b+40=3\left(b+8\right)b\)

\(\Leftrightarrow\left[{}\begin{matrix}b=2\\b=-\dfrac{20}{3}\end{matrix}\right.\)

TH1: \(b=2\Leftrightarrow...\)

TH2: \(b=-\dfrac{20}{3}\Leftrightarrow...\)

(  ) x 9999 x 9999 x 9999 x ... ( có 1000 số 9999 )  x 38 x 45 x 36 x 25 x 58 x 69 x 245 x 246 x 213 x 222 x 546 x 8312 x 999 x 454 x 9999 x 789 x 2563 x 0 x 25 x 24 x 23 x 26 258 x 256 256 x 256 x 24531 x 55 x ( 45 x 1 + 45 x 2 + 45 x 3 + ... + 45 x 1000 +  45 x 1001 + ... + 45 x 9999 ) = 0 nhé

/HT\

(  ) x 9999 x 9999 x 9999 x ... ( có 1000 số 9999 )  x 38 x 45 x 36 x 25 x 58 x 69 x 245 x 246 x 213 x 222 x 546 x 8312 x 999 x 454 x 9999 x 789 x 2563 x 0 x 25 x 24 x 23 x 26 258 x 256 256 x 256 x 24531 x 55 x ( 45 x 1 + 45 x 2 + 45 x 3 + ... + 45 x 1000 +  45 x 1001 + ... + 45 x 9999 ) =  0

HT

@@@@@@@

  ) x 9999 x 9999 x 9999 x ... ( có 1000 số 9999 )  x 38 x 45 x 36 x 25 x 58 x 69 x 245 x 246 x 213 x 222 x 546 x 8312 x 999 x 454 x 9999 x 789 x 2563 x 0 x 25 x 24 x 23 x 26 258 x 256 256 x 256 x 24531 x 55 x ( 45 x 1 + 45 x 2 + 45 x 3 + ... + 45 x 1000 +  45 x 1001 + ... + 45 x 9999 ) = 0 

k cần

1: =>x^2-x=3-x

=>x^2=3

=>x=căn 3 hoặc x=-căn 3

2: =>x^2-4x+3=x^2-4x+4 và x>=2

=>3=4(vô lý)

3: =>2|x-1|=6

=>|x-1|=3

=>x-1=3 hoặc x-1=-3

=>x=-2 hoặc x=4

4: =>|2x-3|=|x-2|

=>2x-3=x-2 hoặc 2x-3=-x+2

=>x=1 hoặc x=5/3

5: =>\(\sqrt{x+2}\left(\sqrt{x-2}+\sqrt{x+2}\right)=0\)

=>x+2=0

=>x=-2

d) \(\frac{4x^2-12x+9}{9-4x^2}=-\frac{\left(2x+3\right)^2}{\left(2x-3\right)\left(2x+3\right)}=\frac{2x+3}{2x-3}\)

\(a/\)

\(4x-4y+x^2-2xy+y^2\)

\(=\left(4x-4y\right)+\left(x^2-2xy+y^2\right)\)

\(=4\left(x-y\right)+\left(x-y\right)^2\)

\(=\left(x-y\right)\left(4+x-y\right)\)

\(b/\)

\(x^4-4x^3-8x^2+8x\)

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

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

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

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

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

\(d/\)

\(x^4-x^2+2x-1\)

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

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

\(e/\)(Xem lại đề)

\(x^4+x^3+x^2+2x+1\)

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

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

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

\(f/\)

\(x^3-4x^2+4x-1\)

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

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

\(=[\sqrt{x}\left(x-2\right)]^2-1\)

\(=[\sqrt{x}\left(x-2\right)-1][\sqrt{x}\left(x-2\right)+1]\)

\(c/\)

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

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

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

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

\(=\left(x-2\right)[\left(x^2+x\right)+\left(2x+2\right)]\)

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

a) \(4x-4y+x^2-2xy+y^2\)

\(=4\left(x-y\right)+\left(x-y\right)^2\)

\(=\left(x-y\right)\left(4+x-y\right)\)

b) \(x^4-4x^3-8x^2+8x\)

\(=x^4+2x^3-6x^3-12x^2+4x^2+8x\)

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

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

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

c) \(x^3+x^2-4x-4\)

\(=x^3-2x^2+3x^2-6x+2x-4\)

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

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

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

\(=\left(x-2\right)\left[x\left(x+2\right)+\left(x+2\right)\right]\)

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

d) \(x^4-x^2+2x-1\)

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

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

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

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

e)Sửa đề \(x^4+x^3+x^2-1\)

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

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

f) \(x^3-4x^2+4x-1\)

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

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

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

`(x - 2)/3 = (x + 1)/4`

`(x - 2) . 4 = (x + 1) . 3`

`<=> 4x - 8 = 3x + 3`

`<=> 4x - 3x = 3 + 8`

`<=> (4 - 3)x = 11`

`=> x = 11`

`=>` `x = 11`

???

:)?????