\(VT=x^4+2x^3+x^2+x^2+x+7>x^4+2x^3+x^2=\left(x^2+x\right)^2\)
\(VT=\left(x^2+x+3\right)^2-\left(5x^2+5x+2\right)< \left(x^2+x+3\right)^2\)
\(\Rightarrow\left(x^2+x\right)^2< y^2< \left(x^2+x+3\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}y^2=\left(x^2+x+1\right)^2\\y^2=\left(x^2+x+2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^4+2x^3+2x^2+x+7=\left(x^2+x+1\right)^2\\x^4+2x^3+2x^2+x+7=\left(x^2+x+2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+x-6=0\\2x^2+3x-3=0\end{matrix}\right.\)
\(\Leftrightarrow...\)
