How to solve: $x^4+x^2=1$

Question

I solved $x^4+x^2+1=0$. But, the above one is hard. The equation is too hard for me to understand. Can anyone solve it? Please help.

Answer 1

$$x^4+x^2=1$$

put $x^2=t$ And you'll have a quadratic in $t$ $$t^2+t-1=0$$ using quadratic formula we get $$t=\frac{-1\pm\sqrt{1+4}}{2}=\frac{-1\pm\sqrt{5}}{2}$$

Now you can find $x$ using $x^2=t$ we get

$$x=\pm\sqrt{\frac{\sqrt5-1}{2}},\pm i\sqrt{\frac{\sqrt5+1}{2}}$$ where $i=\sqrt{-1}$