已知a=5-1,则2a3+7a2-2a-12的值等于_.

问题描述:

已知a=

5
-1,则2a3+7a2-2a-12的值等于______.

由已知得(a+1)2=5,所以a2+2a=4
则原式=2a3+4a2+2a+3a2-4a-12
=2a(a2+2a+1)+3a2-4a-12
=2a(a+1)2+3a2-4a-12
=2a×5+3a2-4a-12
=3a2+6a-12
=3(a2+2a)-12
=3×4-12
=0
故答案0