Question

a2-3a+1=0,求a3+1/a3的值

Answer 1

a2-3a+1=0
显然a=0不能满足要求，因此两边都除以a，
=>
a+1/a-3=0
=>a+1/a=3
a^2+1/a^2=(a+1/a)^2-2=3^2-2=7

a^3+1/a^3
=(a+1/a)(a^2+1/a^2-1)
=3*(7-1)
=18

Answer 2

(a2-3a+1)/a=a-3+(1/a)=0；a+(1/a)=3;
(a+1/a)29=a2+2+1/a2=9；a2+1/a2=7；
a3+1/a3=(a+1/a)(a2-1+1/a2)=3*6=18

Answer 3

a^2-3a+1=0各除以a => a-3+(1/a)=0 => a+(1/a)=3

两边平方 a^2+ 2a*1/a+1/a^2=9 => a^2+2+ 1/a^2=9=>a^2+1/a^2=7

[a^3+ (1/a^3)]=(a+ 1/a)(a^2-a*1/a +1/a^2)=3(a^2- 1 +1/a^2)=3(7-1)=18