> 数学 >
a
7
−1
,则代数式3a3+12a2-6a-12的值为 ___ .
人气:494 ℃ 时间:2019-08-21 05:37:19
解答
∵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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