Question

已知实数x满足x+x^-1=3，则x

1

2

+x-

1

2

=

5

．

Answer 1

分析：设x

1

2

+x-

1

2

=t＞0，将其平方即可求出．

解答：解：设x

1

2

+x-

1

2

=t＞0，则t²=x+x^-1+2=5，∴t=

5

．
故答案为

5

．

点评：熟练掌握指数幂的运算是解题的关键．