Question

已知x平方-3x+1=0,求下列各式的值（1）x+x的-1次方（2）x²+x的-2次方

Answer 1

x^2-3x+1=0

两边同除x

x-3+1/x=0

x+1/x=3

(x+1/x)^2=9

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

x^2+1/x^2=7

所以

（1）x+x^(-1)

=x+1/x

=3

（2）x²+x^(-2)

=x^2+1/x^2

=7