a²-3a-1=0
a²-1=3a
a-1/a=3
﹙1﹚﹙a-1/a﹚²=3²
a²+1/a²=11
﹙2﹚a³-1/a³=﹙a-1/a﹚﹙a²+1+1/a²﹚
=3×﹙11+1﹚
=36
﹙3﹚a³+1/a³=﹙a+1/a﹚﹙a²-1+1/a²﹚
=﹙11-1﹚﹙a+1/a﹚
=10﹙a+1/a﹚
∵ a²+1/a²=11
∴ a²+2+1/a²=13
﹙a+1/a﹚=±√13
∴ a³+1/a³=±10√13.
a²-3a-1=0
a²-1=3a
a-1/a=3
﹙1﹚﹙a-1/a﹚²=3²
a²+1/a²=11
﹙2﹚a³-1/a³=﹙a-1/a﹚﹙a²+1+1/a²﹚
=3×﹙11+1﹚
=36
﹙3﹚a³+1/a³=﹙a+1/a﹚﹙a²-1+1/a²﹚
=﹙11-1﹚﹙a+1/a﹚
=10﹙a+1/a﹚
∵ a²+1/a²=11
∴ a²+2+1/a²=13
﹙a+1/a﹚=±√13
∴ a³+1/a³=±10√13.