若a是方程x2-3x+1=0的根,求2a2-5a-2+3/a2+1=_.

问题描述:

若a是方程x2-3x+1=0的根,求2a2-5a-2+

3
a2+1
=______.

∵a是方程x2-3x+1=0的根,
∴a2-3a+1=0,
∴a2+1=3a,
∴a+

1
a
=3,
∴2a2-5a-2+
3
a2+1
=2a2-6a+a-2+
3
a2+1
=-2-2+a+
1
a
=-1,
故答案为:-1.