Question

已知x^2-5x+1=0，求（x^4+1)/x^2的值

在线等，加分啊

Answer 1

(x^4+1)/x^2
=(x^4)/(x^2)+1/(x^2)
=x^2+1/x^2-----配方
=(x+1/x)^2-2
因为x^2-5x+1=0
(x-5)x=-1
x=1/(5-x)
1/x=5-x
所以(x+1/x)^2-2
=(x+5-x)^2-2
=5^2-2
=23
所以(x^4+1)/x^2=23

Answer 2

x^2-5x+1=0得x^2=5x-1
所以x^4=25x^2-10x+1=25(5x-1)-10x+1=115x-23=23(5x-1)
代入得（x^4+1)/x^2=23(5x-1)/(5x-1)=23