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

=>\(8-12x+6x^2-x^3+8+12x+6x^2+x^3-12x\left(x+1\right)=0\)

=>\(12x^2+16-12x^2-12x=0\)

=>16-12x=0

=>4-3x=0

=>x=4/3

b: 

1: \(\Leftrightarrow2x\left(x+2\right)=0\)

=>x=0 hoặc x=-2

a: \(x^2+12x+36=0\)

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

\(\Leftrightarrow x+6=0\)

hay x=-6

b: Ta có: \(x^2-1=0\)

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

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

c: Ta có: \(25x^2-9=0\)

\(\Leftrightarrow\left(5x-3\right)\left(5x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\\x=-\dfrac{3}{5}\end{matrix}\right.\)

Lời giải:
a. $x^2+12x+36=0$

$\Leftrightarrow (x+6)^2=0$

$\Leftrightarrow x+6=0$

$\Leftrightarrow x=-6$

b.

$x^2-1=0$

$\Leftrightarrow (x-1)(x+1)=0$
$\Leftrightarrow x-1=0$ hoặc $x+1=0$

$\Leftrightarrow x=1$ hoặc $x=-1$

c. 

$25x^2-9=0$

$\Leftrightarrow (5x)^2-3^2=0$

$\Leftrightarrow (5x-3)(5x+3)=0$

$\Leftrightarrow 5x-3=0$ hoặc $5x+3=0$

$\Leftrightarrow x=\frac{3}{5}$ hoặc $x=-\frac{3}{5}$

Chọn đáp án B.

Ta có:

Chọn đáp án B.

Ta có:

Ta có B = x x + x + 1 x − 1 x + x + 1 + x + 3 x − 1 . x − 1 2 x + x − 1

= x x − 1 + x + 3 x − 1 . x − 1 x + 1 2 x − 1 x + 1 = 2 x + 3 x − 1 . x − 1 2 x − 1 = 2 x + 3 2 x − 1    

Vì x ≥ 0  nên  2 x + 3 > 0 , do đó B<0 khi  2 x − 1 < 0 ⇔ x < 1 4 .

Mà  x ≥ 0 ;   x ≠ 1  và  x ≠ 1 4  nên ta được kết quả  0 ≤ x < 1 4 .

a) (x-2)³ - 6(x+1)² - x³ + 12 = 0 

<=> x³-6x²+12x-8-6(x²+2x+1)-x³+12=0

<=> x³-6x²+12x-8-6x²-12x-6-x³+12=0

<=> -12x²+4=0

<=> \(x=\frac{1}{\sqrt{3}},x=-\frac{1}{\sqrt{3}}\)

vậy pt có 2 nghiệm....

b) x³ - 6x² + 12x - 8 = 0 

<=> (x³-2x²)-(4x²-8x)+(4x+8)=0

<=> (x-2)(x²-4x+4)=(x-2)³=0

=> x=2 là nghiệm

c) 8x³ - 12x² + 6x - 1 = 0

<=> (2x-1)³=0

<=> x=1/2

a) \(\left(x-2\right)^3-6\left(x+1\right)^2-x^3+12=0\)

\(\Leftrightarrow x^3-6x^2+12x-8-6\left(x^2+2x+1\right)-x^3+12=0\)

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

\(\Leftrightarrow-12x^2-2=0\)

\(\Leftrightarrow-2\left(6x^2+1\right)=0\)

\(\Leftrightarrow6x^2+1=0\) (vô nghiệm)

Vậy không có giá trị nào của x thỏa mãn pt

b) \(x^3-6x^2+12x-8=0\)

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

\(\Leftrightarrow x-2=0\)

\(\Leftrightarrow x=2\)

Vậy x=2

c) \(8x^3-12x^2+6x-1=0\)

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

\(\Leftrightarrow2x-1=0\Leftrightarrow x=\frac{1}{2}\)

Vậy \(=\frac{1}{2}\)

\(\left(x-2-x\right)\left(x^2-4x+4+x^2-2x+x^2\right)-6x^2-12x-6+12=0\)

\(-2\left(2x^2-6x+4\right)-6x^2-12x+6=0\)

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

-10x^2-2=0

5x^2+1=0

x^2=-1/5

x=\(\varnothing\)

a) x² + 10x + 16 = 0

<=> x² + 2x + 8x + 16 = 0

<=> x( x + 2 ) + 8( x + 2 ) = 0

<=> ( x + 2 )( x + 8 ) = 0

<=> \(\orbr{\begin{cases}x+2=0\\x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-8\end{cases}}\)

b) 4x² - 12x - 7 = 0

<=> 4x² + 2x - 14x - 7 = 0

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

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

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

a. \(x^2+10x+16=0\)

\(\Leftrightarrow x^2+8x+2x+16=0\)

\(\Leftrightarrow x\left(x+8\right)+2\left(x+8\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-8\end{cases}}\)

b. \(4x^2-12x-7=0\)

\(\Leftrightarrow4x^2+2x-14x-7=0\)

\(\Leftrightarrow2x\left(2x+1\right)-7\left(2x+1\right)=0\)

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

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

             Bài làm :

 \(\text{a) }x^2+10x+16=0\)

\(\Leftrightarrow x^2+8x+2x+16=0\)

\(\Leftrightarrow x\left(x+8\right)+2\left(x+8\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-8\end{cases}}\)

 \(\text{b) }4x^2-12x-7=0\)

\(\Leftrightarrow4x^2+2x-14x-7=0\)

\(\Leftrightarrow2x\left(2x+1\right)-7\left(2x+1\right)=0\)

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

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