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....