若a2=a+1,b2=b+1,且a≠b,则a5+b5=_.

问题描述:

若a2=a+1,b2=b+1,且a≠b,则a5+b5=______.

∵a2=a+1,b2=b+1,
∴a2-b2=a-b,
∴a+b=0,
∴a5+b5=(a+b)(a4-a3b+a2 b-ab3+b4)=0.