问题 填空题
a=
7
-1
,则代数式3a3+12a2-6a-12的值为______.
答案

∵a=

7
-1,即a+1=
7

∴3a3+12a2-6a-12=3(a3+4a2-2a-4)=3(a3+a2+3a2+3a-5a-5+1)

=3[a2(a+1)+3a(a+1)-5(a+1)+1]

=3×[(

7
-1)2×
7
+3(
7
-1)×
7
-5
7
+1]

=3(8

7
-14+21-3
7
-5
7
+1)

=3×8

=24.

故答案为:24

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