I have a algebraic equation like so:(adsbygoogle = window.adsbygoogle || []).push({});

x^2-1-εx=0

the roots are obviously-

x=ε/2±√(1+ε^2/4)

How can I expand the expression for the roots- as a taylor series?

the answer is given as:

x(1)=1+ε/2+ε^2/8+O(ε^3)

I am assuming the author expanded the root 'x' in terms of ε before hand and substituted in the algebraic.Is that even allowed?

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# Talor series expansion of roots of algebraic equation

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