..已知:a+1/a=1,求a^2004+1/a^2004

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..已知:a+1/a=1,求a^2004+1/a^2004..已知:a+1/a=1,求a^2004+1/a^2004..已知:a+1/a=1,求a^2004+1/a^2004{一}a+1/a=1(a+

..已知:a+1/a=1,求a^2004+1/a^2004
..已知:a+1/a=1,求a^2004+1/a^2004

..已知:a+1/a=1,求a^2004+1/a^2004
{一}a+1/a=1
(a+1/a)^2=1
a^2+1/a^2+2=1
{二}a^2+1/a^2=-1
(a^2+1/a^2)(a+1/a)=a^3+1/a^3+1/a+a=-1
{三}a^3+1/a^3=-2
(a^3+1/a^3)(a+1/a)=-2
{四}a^4+1/a^4=-2+1=-1
(a^4+1/a^4)(a+1/a)=-1
{五}a^5+1/a^5=-1+2=1
.(4个一循环)
所以a^2004+1/a^2004=-1