问题 填空题
已知x+y=12,xy=9,且x<y,则
x
1
2
-y
1
2
x
1
2
+y
1
2
=______.
答案

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

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