已知a2+3a+1=0,求3a3+(a2+5)(a2-1)-a(5a+6)的值.
问题描述:
已知a2+3a+1=0,求3a3+(a2+5)(a2-1)-a(5a+6)的值.
答
∵a2+3a+1=0,
∴a2+3a=-1,
∴原式=3a3+(a2+5)(a2-1)-a(5a+6)
=3a3+a4+4a2-5-5a2-6a
=a4+3a3+4a2-5-5a2-6a
=a2(a2+3a)+4a2-5-5a2-6a
=-a2+4a2-5-5a2-6a
=-2a2-6a-5
=-2(a2+3a)-5
=-2×(-1)-5
=-3.