\(x\left(x^2+x+1\right)=8\left(x^2+x+1\right)\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x^2+x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}=0\left(vô-nghiệm\right)\end{matrix}\right.\)

1/8x + 3/8x - 5/3 = 2

=> (1/8 + 3/8)x = 2+5/3

=> 1/2x = 11/3

=> x = 11/3:1/2

=> x = 22/3

Vậy x = 22/3

\(x^4-8x^3+11x^2+8x-12=0\)

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

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

\(\Leftrightarrow x=\left\{1;-1;6;2\right\}\)

\(x^4-8x^3+11x^2+8x-12=0\)

\(\Leftrightarrow x^4-x^3-7x^3+7x^2+4x^2-4x+12x-12=0\)

\(\Leftrightarrow\left(x^4-x^3\right)-\left(7x^3-7x^2\right)+\left(4x^2-4x\right)+\left(12x-12\right)=0\)

\(\Leftrightarrow x^3\left(x-1\right)-7x^2\left(x-1\right)+4x\left(x-1\right)+12\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3-7x^2+4x+12\right)=0\)

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

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

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

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

\(\Leftrightarrow\)x - 1 =0 ; x + 1 = 0 ; x - 2 =0 hoặc x - 6 = 0

\(\Leftrightarrow\)x = 1 ; x = -1 ; x = 2 ; x=6

x=-2

X=2

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

\(\Leftrightarrow2x\left(x^2+4x+4\right)-8x^2=2\left(x^3-8\right)\)

\(\Leftrightarrow2x^3+8x^2+8x-8x^2-2x^3+16=0\)

\(\Leftrightarrow8x+16=0\)

\(\Leftrightarrow x=-2\)

\(\Leftrightarrow x^2\left(x-1\right)^2-4\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-1\right)^2\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-2\end{matrix}\right.\)