Question

若x的方-3x+1=0,则x的方/x的四次方+x的方+1的值为

Answer 1

x^2-3x+1=0

二边同除以x:

x+1/x = 3

(x+1/x)^2 = 9 【其中^代表乘方】

x^2+1/x^2+2 = 9

x^2+1/x^2+1 = 8

1/(x^2+1/x^2+1) = 1/8

x^2/(x^4+1+x^2) = 1/8

x^2/(x^4+x^2+1) = 1/8