已知a²+3a+1=0,求3a³+(a²+5) (a²-1)-a(5a+6)的值.

已知a²+3a+1=0,求3a³+(a²+5) (a²-1)-a(5a+6)的值.
已知a²+3a+1=0,求3a³+(a²+5) (a²-1)-a(5a+6)的值.

已知a²+3a+1=0,求3a³+(a²+5) (a²-1)-a(5a+6)的值.
已知a²+3a+1=0,
a²=-3a-1
3a³+(a²+5) (a²-1)-a(5a+6)的值.
=3a(-3a-1)+(-3a-1+5) (-3a-1-1)-5a²-6a
=-9a²-3a+(-3a+4) (-3a-2)-5a²-6a
=-14a²-9a+9a²+6a-12a-8
=-5a²-15a-8
=-5(-3a-1)-15a-8
=15a+5-15a-8
=-3

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

3a³+(a²+5) (a²-1)-a(5a+6)
=3a³+a的4次方+4a²-5-5a²-6a
=a的4次方+3a³+a²-2a²-6a-2+2
=a²(a²+3a+1)-2(a²+3a+1)+2
∵a²+3a+1=0
∴原式=0+0+2=2