\(\Leftrightarrow x^4+x^3+2x^3+2x^2+2x^2+2x+x+1=0\)
\(\Leftrightarrow x^3\left(x+1\right)+2x^2\left(x+1\right)+2x\left(x+1\right)+\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+2x^2+2x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+x^2+x^2+x+x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[x^2\left(x+1\right)+x\left(x+1\right)+x+1\right]=0\)
\(\Leftrightarrow\left(x+1\right)^2\left(x^2+x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2+x+1=0\left(loai\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-1\)
Ta có : \(x^4+3x^3+4x^2+3x+1=0\)
\(\Leftrightarrow x^4+x^3+2x^3+2x^2+2x^2+2x+x+1=0\)
\(\Leftrightarrow x^3\left(x+1\right)+2x^2\left(x+1\right)+2x\left(x+1\right)+x+1=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+2x^2+2x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)^2\left(x^2+x+1\right)=0\)
Vì \(x^2+x+1>0\)
\(\Rightarrow\left(x+1\right)^2=0\)
\(\Rightarrow x=-1\)
Vậy S={-1}
