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