Question

m2+m-1=0,n2-n-1=0代数式m3+n3+2m2-2n2+2008的值

Answer 1

m2+m-1=0,n2-n-1=0代数式m3+n3+2m2-2n2+2008的值

m2+m-1=0,n2-n-1=0

m^2+m=1,n^2-n=1

m3+n3+2m2-2n2+2008

=m^3+m^2+m^3-m^2+m^2-m^2+2008

=m(m^2+m)+n(n^2-n)+m^2-n^2+2008

=m+n+m^2-n^2+2008

=(m^2+m)-(n^2-n)+2008

=1-1+2008

=2008