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

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

\(\Rightarrow x^3+2^3+3.2.x^2+3.2^2.x=0\)

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

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

=>-7x^2+2+7x^2+14x=8

=>14x=6

=>x=3/7

=(x - 2)³ = 0

x = 2

x=0 hoặc x=2/3

x=2 đó bạn

a: \(=\dfrac{3\left(x-2\right)}{\left(x-2\right)^3}=\dfrac{3}{\left(x-2\right)^2}\)

b: \(=\dfrac{x^2\left(x+2\right)}{\left(x+2\right)^3}=\dfrac{x^2}{\left(x+2\right)^2}\)

1) \(8x^3-12x^2+6x-1=0\)

\(\Leftrightarrow\left(2x\right)^2-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3=0\)

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

\(\Leftrightarrow2x-1=0\)

\(\Leftrightarrow2x=1\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

2) \(x^3-6x^2+12x-8=27\)

\(\Leftrightarrow x^3-3\cdot x^2\cdot2+3\cdot2^2\cdot x-2^3=27\)

\(\Leftrightarrow\left(x-2\right)^3=27\)

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

\(\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=3+2\)

\(\Leftrightarrow x=5\)

3) \(x^2-8x+16=5\left(4-x\right)^3\)

\(\Leftrightarrow\left(x-4\right)^2=5\left(4-x\right)^3\)

\(\Leftrightarrow\left(4-x\right)^2=5\left(4-x\right)^3\)

\(\Leftrightarrow5\left(4-x\right)=1\)

\(\Leftrightarrow4-x=\dfrac{1}{5}\)

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

\(\Leftrightarrow x=\dfrac{19}{5}\)

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

\(\Leftrightarrow8-12x+6x^2-x^3=6x^2-12x\)

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

\(\Leftrightarrow8-x^3=0\)

\(\Leftrightarrow x^3=8\)

\(\Leftrightarrow x^3=2^3\)

\(\Leftrightarrow x=2\)

5) \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-10\)

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-10\)

\(\Leftrightarrow\left(x^3-x^3\right)+\left(3x-3x\right)+\left(3x^2+3x^2\right)+\left(1+1\right)-6x^2+12x-6=-10\)

\(\Leftrightarrow0+0+0+\left(6x^2-6x^2\right)+12x-4=-10\)

\(\Leftrightarrow12x-4=-10\)

\(\Leftrightarrow12x=-10+4\)

\(\Leftrightarrow12x=-6\)

\(\Leftrightarrow x=\dfrac{-6}{12}\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

6) \(\left(3-x\right)^3-\left(x+3\right)^3=36x^2-54x\)

\(\Leftrightarrow27-27x+9x^2-x^3-x^3-9x^2-27x-27=36x^2-54x\)

\(\Leftrightarrow-54x-2x^3=36x^2-54x\)

\(\Leftrightarrow-2x^3=36x^2\)

\(\Leftrightarrow-2x^3-36x^2=0\)

\(\Leftrightarrow-2x^2\left(x+18\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-2x^2=0\\x+18=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-18\end{matrix}\right.\)

Bài 1:

\(D=\dfrac{5x^2-30x+53}{x^2-6x+10}=\dfrac{5\left(x^2-6x+10\right)+3}{x^2-6x+10}=5+\dfrac{3}{x^2-6x+10}\)

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

Ta có: \(\left(x+3\right)^2+1\ge1\Rightarrow\dfrac{3}{\left(x-3\right)^2+1}\le3\)

\(\Rightarrow D\le3+5=8\)

Vậy max D= 8 <=> x=3

Bài 2: 

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

\(\Leftrightarrow\left[2\left(x-3\right)^3\right]=-x^3+3.2x^2-3.2^2x+2^3\)

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

\(\Leftrightarrow2x-6=2-x\)

\(\Leftrightarrow3x=8\Leftrightarrow x=\dfrac{8}{3}\)

Vậy tập nghiệm : \(S=\left\{\dfrac{8}{3}\right\}\)

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=\(\varnothing\)