Question

已知x+y=12，xy=9，且x＜y，则

x 1 2 -y 1 2

x 1 2 +y 1 2

=______．

Answer 1

由题设0＜x＜y
∵xy=9，∴

xy

=3
∴x+y-2

xy

=(x

1

2

-y

1

2

)2=12-6=6
x+y+2

xy

=(x

1

2

+y

1

2

)2=12+6=18
∴x

1

2

-y

1

2

=-

6

，x

1

2

+y

1

2

=3

2

∴

x 1 2 -y 1 2

x 1 2 +y 1 2

=

- 6

3 2

=-

3

3

故答案为：-

3

3