document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #184787 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
I think I understand what you are saying.
\n" ); document.write( "Let f(x) and g(x) be two polynomials with integer coefficients.
\n" ); document.write( "Since $\"a\"$ was given to us as a zero,
\n" ); document.write( " $\"f%28x%29%2Aa+=+g%28x%29\"$
\n" ); document.write( "multiply both sides by $\"a%5E%28-1%29\"$ to get
\n" ); document.write( " $\"f%28x%29+=+g%28x%29%2Aa%5E%28-1%29%7D%7D%0D%0ANow+it+seems+that+%7B%7B%7Ba%5E%28-1%29\"$ is also algebraic since it is the zero for f(x).\r
\n" ); document.write( "\n" ); document.write( "Is that what you were needing? \n" ); document.write( "

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