Ta có : \(x^2-2x-1=0 \)
\(\Leftrightarrow \)\((x-1)^2=2\)
\(\Leftrightarrow \)\(\left[\begin{array}{} x-1=\sqrt{2}\\ x-1=-\sqrt{2} \end{array} \right.\)
Đặt P = \(\dfrac{x^6-6x^5+12x^4-8x^3+2015}{x^6-8x^3-12x^2+6x+2015}\)
          =\(\dfrac{(x^6-2x^5-x^4)-(4x^5-8x^4-4x^3)+(5x^4-10x^3-5x^2)-(2x^3-4x^2-2x)+(x^2-2x-1)+2016} {(x^6-2x^5-x^4)+(2x^5-4x^4-2x^3)+(5x^4-10x^3-5x^2)+(4x^3-8x^2-4x)+(x^2-2x-1)+12x+2016}\)
         =\(\dfrac{x^4(x^2-2x-1)-4x^3(x^2-2x-1)+5x^2(x^2-2x-1)-2x(x^2-2x-1)+(x^2-2x-1)+2016} {x^4(x^2-2x-1)+2x^3(x^2-2x-1)+5x^2(x^2-2x-1)+4x(x^2-2x-1)+(x^2-2x-1)+12x+2016}\)
         =\(\dfrac{2016}{12x + 2016}\)
         =\(\dfrac{2016}{12(x+1)+2004}\)
         =\(\dfrac{168}{x+1+167}\)
         =\(\left[\begin{array}{} \dfrac{168}{\sqrt{2}+167}\\ \dfrac{168}{-\sqrt{2}+167} \end{array} \right.\)
Chú thích: Hình như mẫu là \(-6x\) chứ không phải \(6x \) bạn ạ. Hay là mình phân tích sai thì cho mình xin lỗi nhé.

giup minh voi dang can

c: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

a) x = 8 3 .                            b) x = − 9 20 .  

\(\Leftrightarrow x\cdot\dfrac{5}{2}-3x^2+15-18x+12x-2+\dfrac{1}{4}x+3=0\)

\(\Leftrightarrow-3x^2-\dfrac{13}{4}x+16=0\)

\(\Leftrightarrow-12x^2-13x+64=0\)

hay \(x\in\left\{1,83;-2,91\right\}\)

a, \(x^2-12x-2x+24=0\Leftrightarrow x^2-14x+24=0\Leftrightarrow\left(x-12\right)\left(x-2\right)=0\)

TH1 : x = 12 ; TH2 : x = 2 

b, \(x^2-5x-24=0\Leftrightarrow\left(x-8\right)\left(x+3\right)=0\)

TH1 : x = 8 ; TH2 : x = -3 

c, \(4x^2-12x-7=0\Leftrightarrow\left(2x+1\right)\left(2x-7\right)=0\)

TH1 : x = -1/2 ; TH2 : x = 7/2

d, \(x^3+6x^2+12x+8=0\Leftrightarrow\left(x+2\right)^3=0\Leftrightarrow x=-2\)

Tương tự HĐT thôi :)

a) x² - 12x - 2x + 24 = 0

<=> x( x - 12 ) - 2( x - 12 ) = 0

<=> ( x - 12 )( x - 2 ) = 0

<=> \(\orbr{\begin{cases}x-12=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=12\\x=2\end{cases}}\)

b) x² - 5x - 24 = 0

<=> x² + 3x - 8x - 24 = 0

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

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

<=> \(\orbr{\begin{cases}x+3=0\\x-8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=8\end{cases}}\)

c) 4x² - 12x - 7 = 0

<=> 4x² + 2x - 14x - 7 = 0

<=> 2x( 2x + 1 ) - 7( 2x + 1 ) = 0

<=> ( 2x + 1 )( 2x - 7 ) = 0

<=> \(\orbr{\begin{cases}2x+1=0\\2x-7=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{7}{2}\end{cases}}\)

d) x³ + 6x² + 12x + 8 = 0

<=> ( x + 2 )³ = 0

<=> x + 2 = 0

<=> x = -2

e) ( x + 2 )² - x² + 4 = 0

<=> x² + 4x + 4 - x² + 4 = 0

<=> 4x + 8 = 0

<=> 4x = -8

<=> x = -2

f) 2( x + 5 ) = x² + 5x

<=> x² + 5x - 2x - 10 = 0

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

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

<=> \(\orbr{\begin{cases}x+5=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-5\\x=2\end{cases}}\)

m) 16( 2x - 3 )² - 25( x - 5 )² = 0

<=> 4²( 2x - 3 )² - 5²( x - 5 )² = 0

<=> [ 4( 2x - 3 ) ]² - [ 5( x - 5 ) ]² = 0

<=> ( 8x - 12 )² - ( 5x - 25 )² = 0

<=> [ 8x - 12 - ( 5x - 25 ) ][ 8x - 12 + ( 5x - 25 ) ] = 0

<=> ( 8x - 12 - 5x + 25 )( 8x - 12 + 5x - 25 ) = 0

<=> ( 3x + 13 )( 13x - 37 ) = 0

<=> \(\orbr{\begin{cases}3x+13=0\\13x-37=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{13}{3}\\x=\frac{37}{13}\end{cases}}\)

n) x² - 6x + 4 = 0

<=> ( x² - 6x + 9 ) - 5 = 0

<=> ( x - 3 )² - ( √5 )² = 0

<=> ( x - 3 - √5 )( x - 3 + √5 ) = 0

<=> \(\orbr{\begin{cases}x-3-\sqrt{5}=0\\x-3+\sqrt{5}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3+\sqrt{5}\\x=3-\sqrt{5}\end{cases}}\)