已知a^2-a-1=0,求代数式a^3-2a+2007的值

已知a^2-a-1=0,求代数式a^3-2a+2007的值

a^3-2a+2007

= a^3 - a^2 - a + a^2 - a + 2007

= a(a^2-a-1) + (a^2-a-1) + 2008

= 2008.
a^2-a-1=0
a^3-a^2-a=0
a^3-a=a^2

a^3-2a+2007
=a^3-a+2007-a
=a^2-a+2007
=a^2-a-1+2008
=0+2008
=2008
a^2-a=1。拦贺咐拍歼a^3-2a+2007=a^3-a^2+a^2-2a+2007=a(a^2-a)+a^2-2a+2007=a+a^2-2a+2007=a^2-a+2007=1+2007=2008。简纯
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