x2-5x+1=0,求x4+1/x2

题目

x2-5x+1=0,求x4+1/x2

答案

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