已知a²-3a-1=0.求(1)a²+1/a²;(2)a³-1/a³;

2个回答

  • 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.