Question

已知x²-3x+1=0,求根号下x²+1/x²-2的值

Answer 1

x^2-3x+1=0

x^2+1=3x

∵x≠0

∴x+1/x=3

两边平方

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

x^2+1/x^2=7

∴x^2+1/x^2-2=7-2=5

∴√(x^2+1/x^2-2)=√5