We can write the equation
\[x^4-8x^2+12=0 \]
by substituting \[y= x^2\]
. The equation becomes \[y^2-8y+12=0\]
.This equation factorises as
\[(y-6)(y-2)=0\]
.Set each factor equal to 0 and solve.
\[y-6=0 \rightarrow y=6\]
\[y-2=0 \rightarrow y=2\]
\[y=6\]
then \[x^2=6 \rightarrow x= \pm \sqrt{6}\]
.\[y=2\]
then \[x^2 =2 \rightarrow x= \pm \sqrt{2}\]
.