Question

若x²-5x+1=0，則2x2-9x+3+

5

x2+1

=

 

．

Answer 1

分析：首先對代數(shù)式x²-5x+1=0進(jìn)行變形，然后把x²+1=5x，

1

x

=5-x，x²-5x=-1整體代入即可．

解答：解：∵x²-5x+1=0，
∴x²+1=5x，x+

1

x

=5，
∴

1

x

=5-x，
∴2x2-9x+3+

5

x2+1

=2x²-9x+3+

1

x

=2x²-9x+3+5-x
=2x²-10x+8
=2（x²-5x）+8
=6．
故答案為6．

點評：此題的解答，用綜合法即可，據(jù)條件進(jìn)行合理變形，再計算．