Question

若x1、x2是一元二次方程3x2+x-1=0的两个根，则(1x1)2+(1x2)2=______

若x1、x2是一元二次方程3x2+x-1=0的两个根，则(1x1)2+(1x2)2=______．

Answer 1

根据题意得x₁+x₂=-

1

3

，x₁?x₂=-

1

3

，
(

1

x1

)2+(

1

x2

)2=

x12+x22

x12?x22

=

(x1+x2)2?2x1x2

(x1x2)2

=

(? 1 3 )2?2×(? 1 3 )

(? 1 3 )2

=7．
故答案为7．