<s>[INST] How to solve this equation, when the unknown variable just disappears? This problem

$\sqrt{1-x^2} + \sqrt{3+x^2} = 2$

has the solution $x = 1$ and $x = -1$.
However, I always get stuck like this:

  
*
  
*$1-x^2 + 3+x^2 = 4$
  
*$4 = 4$
  

How do I isolate that darn unknown?
 [/INST] Square both sides of original equation: $$1-x^2+3+x^2+2\sqrt{(1-x^2)(3+x^2)}=4\Longrightarrow\sqrt{(1-x^2)(3+x^2)}=0\Longrightarrow x =\pm1$$ since $\,3+x^2=0\,$has no real solutions
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