Question

已知x1,x2是一元二次方程x²-4x+1=0的两个实数根,求：(1)(x1+x2)²; (

Answer 1

(1)

x1+x2=4

x1x2=1

(x1+x2)^2

=4^2

=16

(2)

1/x1+1/x2

=(x1+x2)/x1x2

=4/1

=4

(3)

(x1-x2)^2

=x1^2-2x1x2+x2^2

=(x1+x2)^2-4x1x2

=16-4

=12