Question

已知實數x滿足x+x^-1=3，則x

1

2

+x-

1

2

=

5

．

Answer 1

分析：設x

1

2

+x-

1

2

=t＞0，將其平方即可求出．

解答：解：設x

1

2

+x-

1

2

=t＞0，則t²=x+x^-1+2=5，∴t=

5

．
故答案為

5

．

點評：熟練掌握指數冪的運算是解題的關鍵．