a) Ta có: \(A=\left(x+1\right)^4-2\left(x+1\right)^2+5\)
\(=\left(x+1\right)^4-2\left(x+1\right)^2+1+4\)
\(=\left[\left(x+1\right)^2-1\right]^2+4\ge4\forall x\)
Dấu '=' xảy ra khi \(\left(x+1\right)^2=1\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=1\\x+1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)