问题 解答题
已知x-y=
1
2
x2+y2=1
,求x2-y2的值
答案

(x-y)2=

1
4

x2-2xy+y2=

1
4

2xy=1-

1
4
=
3
4

(x+y)2=1+

3
4
=
7
4

x+y=±

7
2

x2-y2=(x+y)(x-y)=±

7
4

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