Question

已知a^2-3a+1=0,求a^2+1/a^2

Answer 1

a^2-3a+1=0;

a=0时,方程不成立,所以a不等于0

两边同除以a

a-3+1/a=0;

a+1/a=3;

(a+1/a)^2=a^2+2a*(1/a)+(1/a)^2=a^2+(1/a)^2+2;

3^2=a^2+(1/a)^2+2;

a^2+(1/a)^2=7