\(x^4+4x^3+4x^2-4=0\)
\(x^2\left(x^2+4x+4\right)=4\)
\(x^2\left(x+2\right)^2=2^2\)
\(\left[x\left(x+2\right)\right]^2=2^2\)
\(\left|x\left(x+2\right)\right|=2\)
TH1:
\(x\left(x+2\right)=2\)
\(x^2+2x=2\)
\(x^2+2x+1=3\)
\(\left(x+1\right)^2=3\)
\(x_1=-1-\sqrt{3}\)
\(x_2=-1+\sqrt{3}\)
TH2:
\(x\left(x+2\right)=-2\)
\(x^2+2x+1=-1\)
\(\left(x+1\right)^2=-1\) vô nghiệm
KL: \(x_1=-1-\sqrt{3}\\ x_2=-1+\sqrt{3}\)
\(x^4+4x^3+4x^2-4=0\)
\(\Rightarrow x^4+4x^3+4x^2=4\)
\(\Rightarrow x^2\left(x^2+4x+4\right)\)
\(\Rightarrow x^2\left(x+2\right)^2=4\)
\(\Rightarrow\left[x\left(x+2\right)\right]^2=4\)
\(\Rightarrow x\left(x-2\right)=\pm2\)
\(\Rightarrow\left[{}\begin{matrix}x\left(x-2\right)=2\\x\left(x-2\right)=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-2x=2\\x^2-2x=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-2x+1=3\\x^2-2x+1=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^2=3\\\left(x-1\right)^2=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^2=\pm\sqrt{3}\\x\in\varnothing\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1+\sqrt{3}\\x=1-\sqrt{3}\end{matrix}\right.\)
