Question

已知实数a是一元二次方程x^2-2006x+z=0的解,求代数式a^2-2005a+2006/a^2+1

Answer 1

因为a^2-2006a+1=0 所以a^2+1=2006a

a^2-2005a+2006/(a^2+1)

=a^2-2005a+2006/2006a

=a^2-2005a+1/a

=a-1+1/a

=(a^2-a+1)/a

=2005a/a

=2005