若x^2-4x+1=0,不解方程求下列各式的值：（1）x+1/x;（2）x^2+1/x^2

Question

若x^2-4x+1=0,不解方程求下列各式的值：（1）x+1/x;（2）x^2+1/x^2

Answer 1

1) x+1/x
=x+（4x-x^2）/x
=x+4-x
=4
2) x^2+1/x^2
=(x+1/x)^2-2
=(4)^2-2
=16-2
=14