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

问题描述:

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

1
x1
+
1
x2
=______.

由题意知,x1+x2=

b
a
=3,x1x2=
c
a
=1,
x12+x22=(x1+x22-2x1x2=9-2=7,
1
x1
+
1
x2
=
x1+x2
x1x2
=3,
故填7;3.