a) \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)

\(\Leftrightarrow\left(x^3+2^3\right)-\left(x^3-2x\right)=15\)

\(\Leftrightarrow x^3+8-x^3+2x=15\)

\(\Leftrightarrow2x+8=15\) 

\(\Leftrightarrow2x=15-8\)

\(\Leftrightarrow2x=7\)

\(\Leftrightarrow x=\dfrac{7}{2}\)

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

\(\Leftrightarrow x^2-8x+16-\left(x^2-4\right)=6\)

\(\Leftrightarrow x^2-8x+16-x^2+4=6\)

\(\Leftrightarrow-8x+20=6\)

\(\Leftrightarrow-8x=6-20\)

\(\Leftrightarrow-8x=-14\)

\(\Leftrightarrow x=\dfrac{7}{4}\) 

c) \(x^4-2x^3+x^2-2x=0\)

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

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

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

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

`(x+2)(x^2 -2x+4) -x(x^2-2)=15`

`<=> x^3 +8 - x^3 + 2x-15=0`

`<=> 2x-7=0`

`<=> 2x=7`

`<=>x=7/2`

__

`(x-4)^2 -(x-2)(x+2)=6`

`<=>x^2 - 8x+16- x^2 +4-6=0`

`<=> -8x+14=0`

`<=> -8x=-14`

`<=>x=14/8= 7/4`

__

`x^4 -2x^3 +x^2-2x=0`

`<=>x(x^3-2x^2+x-2)=0`

`<=> x(x^3+x-2x^2-2)=0`

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

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\4x^2-8x+4=x^2-2x+4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x^2-6x=0\\x\ge1\end{matrix}\right.\Leftrightarrow x=2\)

\(\sqrt{x^2-2x+4}=2x-2\)             Đk: \(2x-2\ge0\Rightarrow x\ge1\)

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

\(\Rightarrow x^2-2x+4=4x^2-8x+4\)

\(\Rightarrow3x^2-6x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

`x(2x-4)-(x-2)(2x+3)=0`

`<=>2x(x-2)-(x-2)(2x+3)=0`

`<=>(x-2)(2x-2x-3)=0`

`<=>(x-2)*(-3)=0`

`<=>x-2=0`

`<=>x=2`

\(a,\Leftrightarrow x^3-8-x\left(x^2-9\right)=1\\ \Leftrightarrow x^3-8-x^3+9x=1\\ \Leftrightarrow9x=9\Leftrightarrow x=1\\ b,\Leftrightarrow8x^3+12x^2+6x+1-8x^3 +12x^2-6x+1-24x^2+24x-1=0\Leftrightarrow1=0\Leftrightarrow x\in\varnothing\)

a) \(\Leftrightarrow x^3-8-x^3+9x=1\)

\(\Leftrightarrow9x=9\Leftrightarrow x=1\)

b) \(\Leftrightarrow8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-24x^2+24x-6=5\)

\(\Leftrightarrow24x=9\Leftrightarrow x=\dfrac{3}{8}\)