$x^2<x^4+3x^2+1<x^4+4x^2+4\Leftrightarrow x^2<y^2<(x+2)^2\Rightarrow y^2=(x+1)^2\Rightarrow (x+1)^2=x^4+3x^2+1\Leftrightarrow x^4+x^2=0\Leftrightarrow x^2(x^2+1)=0\Rightarrow x=0\Rightarrow y=\pm 1$
$
(x
^2)^2<
x^4+3x^2+1<
x^4+4x^2+4\Leftrightarrow
(x^2
)^2<y^2<(x
^2+2)^2\Rightarrow y^2=(x
^2+1)^2\Rightarrow x^4+3x^2+1
=(x^
2+
1)^2\Leftrightarrow x^2=0\
Leftrightarrow x=0\Rightarrow y=\pm 1$