Question

已知a^2-3a+1=0;求a+1\a,a^2+1\a^2,(a-1\a)^2的值

Answer 1

解由a^2-3a+1=0

得a^2+1=3a

即a+1/a=3

故a^2+1/a^2

=(a+1/a)^2-2a×1/a

=3^2-2*1

=7

(a-1a)^2

=a^2+1/a^2-2a×1/a

=a^2+1/a^2+2a×1/a-4a×1/a

=(a+1/a)^2-4

=7-4

=3