Question

已知a+

1

a

=2，a2+

1

a2

=2，a3+

1

a3

=2，則a4+

1

a4

=

 

．

Answer 1

分析：由已知可推出a=1，將a代入，則a4+

1

a4

=2．

解答：解：由已知可得：a=1，故a⁴+

1

a4

=2．故答案為2．

點評：解答此題的關鍵是由已知條件觀察出a的值，再代入代數式即可．