SOLUTION: How can I show that if {{{a}}} is algebraic (which means is zero of a rational polynomial), {{{a^-1}}} is algebraic, too?

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Question 250639: How can I show that if a is algebraic (which means is zero of a rational polynomial), a%5E-1 is algebraic, too?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
I think I understand what you are saying.
Let f(x) and g(x) be two polynomials with integer coefficients.
Since a was given to us as a zero,
f%28x%29%2Aa+=+g%28x%29
multiply both sides by a%5E%28-1%29 to get
f%28x%29+=+g%28x%29%2Aa%5E%28-1%29%7D%7D%0D%0ANow+it+seems+that+%7B%7B%7Ba%5E%28-1%29 is also algebraic since it is the zero for f(x).
Is that what you were needing?