Question
Solve: $x^4 – 2x^2 – 3 = 0.$
✓
Answer
$x^4-2 x^2-3=0$
$\Rightarrow x^4-3 x^2+x^2-3=0 $
$ \Rightarrow x^2\left(x^2-3\right)+1\left(x^2-3\right)=0 $
$ \Rightarrow\left(x^2-3\right)\left(x^2+1\right)=0$
If $x^2-3=0$ or $x^2+1=0$
then $x^2=3$ or $x^2=-1$ (reject)
$\Rightarrow x= \pm \sqrt{3}$
$\Rightarrow x^4-3 x^2+x^2-3=0 $
$ \Rightarrow x^2\left(x^2-3\right)+1\left(x^2-3\right)=0 $
$ \Rightarrow\left(x^2-3\right)\left(x^2+1\right)=0$
If $x^2-3=0$ or $x^2+1=0$
then $x^2=3$ or $x^2=-1$ (reject)
$\Rightarrow x= \pm \sqrt{3}$
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