Question

Giải pt:

\(x^4+2x^3+4x^2+2x+1=0\)

Answer 1

\(x^4+2x^3+4x^2+2x+1=0\)

\(\Leftrightarrow\left(x^4+2x^3+x^2\right)+\left(3x^2+2x+1\right)=0\)

\(\Leftrightarrow\left(x^2+x\right)^2+\left(\sqrt{3}x\right)^2+2.\sqrt{3}x.\frac{1}{\sqrt{3}}+\frac{1}{3}+\frac{2}{3}=0\)

\(\Leftrightarrow\left(x^2+x\right)^2+\left(\sqrt{3}x+\frac{1}{\sqrt{3}}\right)^2+\frac{2}{3}=0\)

Ta dễ thấy \(\left(x^2+x\right)^2+\left(\sqrt{3}x+\frac{1}{\sqrt{3}}\right)^2+\frac{2}{3}>0\forall x\)

Do đó pt trên vô nghiệm