Question

已知x^2一5x+1=0求x^4+1除以x^2的值

Answer 1

有：x^2+1=5x,两边同时除以x得到：x+1/x=5;(x+1/x)^2=x^2+1/(x^2)+2=25

(x^4+1)/x^2=x^2+1/(x^2)=25-2=23

所以答案是23