Question

若x2-4x+1=0,求（1）x+1/x的值；（2）x2+1/x2的值；（3）x-1/x的值；（4）x4*1/x4

Answer 1

x^2-4x+1=0

x^2+1=4x

x+1/x=4

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

x^2+2+1/x^2=16

x^2+1/x^2=14

x^2-2+1/x^2=12

(x-1/x)^2=12

x-1/x=±√12

x-1/x=±2√3

x^2+1/x^2=14

(x^2+1/x^2)^=14^2

x^4+2+1/x^4=196

x^4+1/x^4=194