Question

Giải pt;

x(x+2)(x² +2x+2)+1=0

Answer 1

Ta có: \(x\left(x+2\right)\left(x^2+2x+2\right)+1=0\)

\(\Rightarrow\left(x^2+2x\right)\left[\left(x^2+2x+1\right)+1\right]+1=0\)

\(\Rightarrow\left[\left(x^2+2x+1\right)-1\right]\left[\left(x+1\right)^2+1\right]+1=0\)

\(\Rightarrow\left[\left(x+1\right)^2-1\right]\left[\left(x+1\right)^2+1\right]+1=0\)

\(\Rightarrow\left(x+1\right)^4-1+1=0\Rightarrow\left(x+1\right)^4=0\Rightarrow x+1=0\Rightarrow x=-1\)

Vậy x=-1