Question

已知方程x²-3x+1=0的两根是x₁，x₂；则：x₁²+x₂²=______，

1

x1

+

1

x2

=______．

Answer 1

由题意知，x₁+x₂=-

b

a

=3，x₁x₂=

c

a

=1，
x₁²+x₂²=（x₁+x₂）²-2x₁x₂=9-2=7，

1

x1

+

1

x2

=

x1+x2

x1x2

=3，
故填7；3．