a) \(x^2-12x+11\)\(=0\)

\(\Leftrightarrow\left(x-6\right)^2-25=0\)

\(\Leftrightarrow\left(x-6+5\right)\left(x-6-5\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-11\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-11=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=11\end{matrix}\right.\)

a)\(x^2-12x+11=0\)

\(x^2-x-11x+11=0\)

\(\left(x^2-x\right)-\left(11x-11\right)=0\)

\(x\left(x-1\right)-11\left(x-1\right)=0\)

\(\left(x-1\right)\left(x-11\right)=0\)

\(=>\left[{}\begin{matrix}x-1=0\\x-11=0\end{matrix}\right.\)

\(=>\left[{}\begin{matrix}x=1\\x=11\end{matrix}\right.\)

b)\(4x^2-4x-3=0\)

\(4x^2-2x+6x-3=0\)

\(2x\left(2x-1\right)+3\left(3x-1\right)=0\)

\(\left(2x-1\right)\left(2x+3\right)=0\)

\(=>\left[{}\begin{matrix}2x-1=0\\2x+3=0\end{matrix}\right.\)

\(=>\left[{}\begin{matrix}x=0,5\\x=-1,5\end{matrix}\right.\)\

c)\(4x^2-12x-7=0\)

\(4x^2-14x+2x-7=0\)

\(2x\left(2x-7\right)+\left(2x-7\right)=0\)

\(\left(2x-7\right)\left(2x+1\right)=0\)

\(=>\left[{}\begin{matrix}2x-7=0\\2x+1=0\end{matrix}\right.\)

\(=>\left[{}\begin{matrix}x=3,5\\x=-0,5\end{matrix}\right.\)

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

\(=>\left(x^3-6x^2\right)-\left(8-12x\right)=0\)

\(=>x^3-6x^2-8+12x=0\)

\(x^3-3x^2.2+3x.2^2-2^3=0\)

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

\(=>x-2=0\)

\(=>x=2\)

a,4x^2-4x+1=0

  4x^2-2x-2x+1=0

  2x (2x-1)-(2x-1)=0

  (2x-1)(2x-1)=0

  (2x-1)^2=0

=>2x-1=0 <=> x=1/2

a) \(x\left(x-2\right)-7x+14=0\)

\(\Leftrightarrow x\left(x-2\right)-7\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-7\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=7\end{cases}}\)

b) \(x^2\left(x-3\right)+12-4x=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x=3\\x^2=4\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\pm2\end{cases}}\)

c) \(x^2+12x-13=0\)

\(\Leftrightarrow\left(x^2-x\right)+\left(13x-13\right)=0\)

\(\Leftrightarrow x\left(x-1\right)+13\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+13\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-13\end{cases}}\)

d) \(4x^2-4x=8\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

e) \(x^2-6x=1\)

\(\Leftrightarrow\left(x-3\right)^2=10\)

\(\Leftrightarrow\orbr{\begin{cases}x-3=\sqrt{10}\\x-3=-\sqrt{10}\end{cases}}\Rightarrow\orbr{\begin{cases}x=3+\sqrt{10}\\x=3-\sqrt{10}\end{cases}}\)

a) x( x - 2 ) - 7x + 14 = 0

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

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

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

b) x²( x - 3 ) + 12 - 4x = 0

<=> x²( x - 3 ) - 4( x - 3 ) = 0

<=> ( x - 3 )( x² - 4 ) = 0

<=> \(\orbr{\begin{cases}x-3=0\\x^2-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=\pm2\end{cases}}\)

c) x² + 12x - 13 = 0

<=> x² - x + 13x - 13 = 0

<=> x( x - 1 ) + 13( x - 1 ) = 0

<=> ( x - 1 )( x + 13 ) = 0

<=> \(\orbr{\begin{cases}x-1=0\\x+13=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-13\end{cases}}\)

d) 4x² - 4x = 8

<=> 4( x² - x ) = 8

<=> x² - x = 2

<=> x² - x - 2 = 0

<=> x² + x - 2x - 2 = 0

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

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

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

e) x² - 6x = 1

<=> x² - 6x + 9 = 1 + 9

<=> ( x - 3 )² = 10

<=> ( x - 3 )² = ( ±√10 )²

<=> \(\orbr{\begin{cases}x-3=\sqrt{10}\\x-3=-\sqrt{10}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=3+\sqrt{10}\\x=3-\sqrt{10}\end{cases}}\)

Lời giải:

PT $\Leftrightarrow 8x^3-16x^2+6x+2=0$

$\Leftrightarrow (8x^3-8x^2)-(8x^2-8x)-(2x-2)=0$

$\Leftrightarrow 8x^2(x-1)-8x(x-1)-2(x-1)=0$

$\Leftrightarrow (x-1)(8x^2-8x-2)=0$

$\Leftrightarrow 2(x-1)(4x^2-4x-1)=0$

$\Leftrightarrow x-1=0$ hoặc $4x^2-4x-1=0$

Nếu $x-1=0\Leftrightarrow x=1$ 

Nếu $4x^2-4x-1=0$

$\Leftrightarrow (2x-1)^2-2=0$

$\Leftrightarrow (2x-1-\sqrt{2})(2x-1+\sqrt{2})=0$

$\Leftrightarrow x=\frac{1\pm \sqrt{2}}{2}$

1)(x²-4x+16)(x+4)-x(x+1)(x+2)+3x²=0

\(\Rightarrow\)(x³+64)-x(x²+2x+x+2)+3x²=0

\(\Rightarrow\)x³+64-x³-2x²-x²-2x+3x²=0

\(\Rightarrow\)-2x+64=0

\(\Rightarrow\)-2x=-64

\(\Rightarrow\)x=\(\dfrac{-64}{-2}\)

\(\Rightarrow x=32\)

2)(8x+2)(1-3x)+(6x-1)(4x-10)=-50

\(\Rightarrow\)8x-24x²+2-6x+24x²-60x-4x+10=50

\(\Rightarrow\)-62x+12=50

\(\Rightarrow\)-62x=50-12

\(\Rightarrow\)-62x=38

\(\Rightarrow\)x=\(-\dfrac{38}{62}=-\dfrac{19}{31}\)

3)(x²+2x+4)(2-x)+x(x-3)(x+4)-x²+24=0

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

\(\Rightarrow\)8-x³+x³+4x²-3x²-12x-x²+21=0

\(\Rightarrow\)-12x+29=0

\(\Rightarrow\)-12x=-29

\(\Rightarrow\)x=\(\dfrac{-29}{-12}=\dfrac{29}{12}\)

a: \(x^2+12x+36=0\) 

=>\(x^2+2\cdot x\cdot6+6^2=0\)

=>\(\left(x+6\right)^2=0\)

=>x+6=0

=>x=-6

b: \(4x^2-4x+1=0\)

=>\(\left(2x\right)^2-2\cdot2x\cdot1+1^2=0\)

=>\(\left(2x-1\right)^2=0\)

=>2x-1=0

=>2x=1

=>x=1/2

c: \(x^3+6x^2+12x+8=0\)

=>\(x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=0\)

=>\(\left(x+2\right)^3=0\)

=>x+2=0

=>x=-2