若a^2=a+1,b^2=b+1,且a≠b,则a^5+b^5的值为（ ）.A.5 B.7 C.9 D.11

若a^2=a+1,b^2=b+1,且a≠b,则a^5+b^5的值为（ ）.A.5 B.7 C.9 D.11
若a^2=a+1,b^2=b+1,且a≠b,则a^5+b^5的值为（ ）.A.5 B.7 C.9 D.11

若a^2=a+1,b^2=b+1,且a≠b,则a^5+b^5的值为（ ）.A.5 B.7 C.9 D.11
a²=a+1
a^4=a²+2a+1
a^5=a³+2a²+a
=a(a+1)+2(a+1)+a
=a²+a+2a+2+a
=a+1+a+2a+2+a
=5a+3
同理b^5=5b+3
a^5+b^5=5(a+b)+6
而把a,b可以看成x²=x+1的两个不等的实数根
则：x²-x-1=0
由韦达定理得：a+b=1
则∴a^5+b^5=5(a+b)+6=5+6=11
故而选D