∵a²+3a+1=0，∴a²+3a=-1，∴3a³+(a²+5)(a²-1)-5(a+1)(a-1)-6a=3a³+(a²+5)(a²-1)-5(a²-1)-6a=3a³+a²(a²-1)-6a=a^4+3a³-a²-6a=a²(a²+3a)-a²-6a=-2a²-6a=-2(a²+3a)=2。
