问题 解答题
已知:x=
3
+
2
3
-
2
y=
3
-
2
3
+
2
,求
x
y
+
y
x
+2
的值.
答案

∵x=

3
+
2
3
-
2
=
(
3
+
2
)2
(
3
-
2
)(
3
+
2
)
=
3+2+2
6
3-2
=5+2
6

y=

3
-
2
3
+
2
=
(
3
-
2
)2
(
3
+
2
)(
3
-
2
)
=
3+2-2
6
3-2
=5-2
6

原式=

x2+y2
xy
+2=
x2+y2
xy
+
2xy
xy
=
(x+y)2
xy
=
(5+2
6
+5-2
6
)2
(5+2
6
)(5-2
6
)
=
100
25-24
=100.

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