<s>[INST] Solutions of $x^4+2tx^2+1=0$ 
I am looking for all the solutions of $x^4+2tx^2+1=0$ 
Is there any "quick" way to figure out all the complex-solutions $\pi_i(t)$ where $i=1,...4$ ? 
I got $\pi_1(t)=\sqrt{-t+\sqrt{t^2-1}}\sqrt{t-\sqrt{t^2-1}}\sqrt{-t+\sqrt{1-t^2}}$  but apparently I am too "stupid" to verify my calculation. I always end up making mistakes (hopefully) in my calculation.
Would appreciate any help
 [/INST] $$x^4+2tx^2+1=0$$
Substitute $y=x^2$
$$y^2+2ty+1=0$$
Now use the formula $$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$
So, here $a=1,b=2t,c=1$
$$y=\frac{-t\pm \sqrt{4t^2-4(1)(1)}}{2(1)}$$
$$y=\frac{-t\pm \sqrt{4t^2-4}}{2}$$
$$y=-t\pm \sqrt{t^2-1}$$
Substitute back $y=x^2$
$$x^2=-t\pm \sqrt{t^2-1}$$
$$x=\pm\sqrt{-t\pm \sqrt{t^2-1}}$$
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