\(x^4+2x^3+2x^2+2x+1=0\)
\(\Rightarrow x^4+x^3+x^3+x^2+x^2+x+x+1=0\)
\(\Leftrightarrow x^3\left(x+1\right)+x^2\left(x+1\right)+x\left(x+1\right)+x+1\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+x^2+x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[x^2\left(x+1\right)+x+1\right]=0\Leftrightarrow\left(x+1\right)\left(x^2+1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)^2\left(x^2+1\right)=0\)
Vì \(x^2\ge0\Rightarrow x^2+1>0\)
=> x + 1 = 0
=> x = - 1
VẬy x = -1
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