\(\left(x^2+1\right)^2+3x\left(x^2+1\right)+2x^2=0\)
\(\Leftrightarrow\left(x^2+1\right)^2+2\left(x^2+1\right)^2\frac{3x}{2}+\frac{9x^2}{4}-\frac{x^2}{4}=0\)
\(\Leftrightarrow\left(x^2+1+\frac{3x}{2}\right)^2-\left(\frac{x}{2}\right)^2=0\)
\(\Leftrightarrow\left(x^2+1+\frac{3x}{2}-\frac{x}{2}\right)\left(x^2+1+\frac{3x}{2}+\frac{x}{2}\right)=0\)
\(\Leftrightarrow\left(x^2+x+1\right)\left(x^2+2x+1\right)=0\)
\(\forall x,\)\(x^2+x+1=x^2+2x.\frac{1}{2}+\frac{1}{4}+\frac{3}{4}=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)
\(\Rightarrow x^2+2x+1=0\)
\(\Leftrightarrow\left(x+1\right)^2=0\)
\(\Leftrightarrow x=-1\)
Vậy tập nghiệm của pt là S={-1}
