分类：教育/科学-学习帮助
问题：已知:m^2=m+1,n^2=n+1(m不等于n),求m^5+n? 
已知:m^2=m+1,n^2=n+1(m不等于n),求 m^5+n^5=?
回答：m^2=m+1 (1) 
n^2=n+1 (2) 
(1)-(2)得m+n=1 
m^5+n^5 
=m*m^2*m^2+n*n^2*n^2 
=m*(m+1)^2+n*(n+1)^2 
=m^3+2m^2+m+n^3+2n^2+n 
=m(m+1)+2m^2+m+n(n+1)+2n^2+n 
=3m^2+2m+3n^2+2n 
=5m+3+5n+3 
=5(m+n)+6 
=11