<s>[INST] Rearranging the formula Transpose this formula to make $y$ the subject.
$$x=\sqrt{x^2y^2+1-y}$$
My try:
$$x^2=x^2y^2+1-y$$
$$x^2-x^2y^2=1-y$$
$$x^2(1-y^2)=1-y$$
Here I got 2 $y$ terms, but I am not sure what to do next.
 [/INST] You can write $$0=y^2-\frac{1}{x^2}y+\frac{1-x^2}{x^2}$$ using the quadratic formula we obtain
$$y_{1,2}=\frac{1}{2x^2}\pm\sqrt{\left(\frac{1}{2x^2}\right)^2-\frac{1-x^2}{x^2}}$$
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