问题 解答题
(1)化简
a+1+
a2-1
a+1-
a2-1
+
a+1-
a2-1
a+1+
a2-1
(a>1);
(2)设x,y是实数,且x2+y2-2x+4y+5=0,求
1
(
2
x+
1
2
3
y)
2
的值.
答案

(1)原式=

(a+1+
a2-1
)2+(a+1-
a2-1
)2
(a+1-
a2-1
)(a+1+
a2-1
)

=

[(a+1)2+2(a+1)
a2-1
+a2-1][(a+1)2-2(a+1)
a2-1
+a2-1]
(a+1)2-(a2-1)

=

2(a+1)2+2(a2-1)
a2+2a+1-a2+1

=

2a2+2a
a+1

=

2a(a+1)
a+1

=2a;

(2)x2+y2-2x+4y+5=0

(x-1)2+(y+2)2=0

x-1=0,y+2=0

x=1,y=-2

1
(
2
x+
1
2
3
y)
2

=

1
(
2
-
3
)2

=

1
3
-
2

=

3
+
2

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