Question

如果m、n是两个不相等的实数,且满足m平方-2m=1,n平方-2n=1,那么代数式2m平方+4n平方-4n+1999的值

Answer 1

(m-1)^2=2,m=1±√2,

n=1±√2,

m≠n

m+n=2

又m^2=2m+1

n^2=2n+1

2m平方+4n平方-4n+1999

=2(2m+1)+4(2n+1)-4n+1999

=4(m+n)+2005

=2013