问题 解答题
计算:
(1)(π-1)0+(
1
2
)-1+|5-
27
|-2
3

(2)已知x=
2-
3
2+
3
y=
2+
3
2-
3
,求x2+y2的值.
答案

(1)原式=1+2+

27
-5-2
3

=3+3

3
-5-2
3

=-2+

3

(2)x=

2-
3
2+
3
=
(2-
3
)×(2-
3
)
(2+
3
)×(2-
3
)
=7-4
3

y=

2+
3
2-
3
=7+4
3

x+y=7-4

3
+7+4
3
=14,xy=(7-4
3
)×(7+4
3
)=1,

∴x2+y2=(x+y)2-2xy=142-2×1=194.

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