\(\left(x^2-1\right)\left(x^2+4x+3\right)=192\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+1\right)\left(x+3\right)=192\)

\(\Leftrightarrow\left(x^2+2x-3\right)\left(x^2+2x+1\right)=192\)

\(\text{Đặt }x^2+2x+1=a\left(a\ge0\right)\)

\(\Rightarrow a\left(a-4\right)=192\)

\(\Leftrightarrow\left(a+12\right)\left(a-16\right)=0\)

\(\Rightarrow a=16\)

\(\Rightarrow x^2+2x+1=16\)

\(\Leftrightarrow\left(x-3\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)

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

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

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

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

\(\Rightarrow x=-1\)