已知a²+a-1=0,求a³+2a²+2008的值?

问题描述:

已知a²+a-1=0,求a³+2a²+2008的值?


∵a²+a-1=0
∴a²=1-a
∴a³+2a²+2008
=a(1-a)+2a²+2008
=a²+a+2008
=1+2008
=2009

a²+a-1=0 a²+a=1
a³+2a²+2008=a³-1+2a²+2009=(a-1)(a²+a+1)+2a²+2009=2(a-1)+2a²+2009
=2a+2a²+2009-2=2(a²+a)+2007=2009

结果是一样的,告诉你一个不一样的过程:
a³+2a²+2008
=a³+a²+a²+2008
=a³+a²-a+a+a²+2008
=(a³+a²-a)+(a²+a-1)+1+2008
=a(a²+a-1)+(a²+a-1)+1+2008
=a*0+0+1+2008
=2009
二:
a²+a-1=0 a²+a=1
a³+2a²+2008
=a³+a²+a²+2008
=a(a²+a)+a²+2008
=a+a²+2008
=1+2008
=2009