- #1
marellasunny
- 255
- 3
I have a algebraic equation like so:
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?
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?