Question

已知x^2-5x+1=0,求x^2+1/x^2和x^4+1/x^4的值

Answer 1

x^2-5x+1=0

x-5+1/x=0

x+1/x=5

(x+1/x)^2

=x^2+1/x^2+2=25

x^2+1/x^2=23

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

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

=529

x^4+1/x^4=527