\(x^4+2x^3+2x^2+2x+1=0\)
\(\Leftrightarrow\left(x^4+x^3\right)+\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^3+x^2+x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[\left(x^3+x^2\right)+\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x+1\right)^2\left(x^2+1\right)=0\)
Mà \(x^2+1>0\forall x\)
\(\Rightarrow\left(x+1\right)^2=0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
Vậy x=-1
x4+2x3+2x2+2x+1=0
<=>(x4+2x2+1)+(2x3+2x)=0
<=>(x2+1)2+2x(x2+1)=0
<=>(x2+1)(x2+1+2x)=0
<=>(x2+1)(x+1)2=0
=>(x+1)2=0=>x+1=0=>x=-1
