已知x=5+3,y=5-3,求下列各式的值: (1)x2-2xy+y2 (2)x2-y2.

问题描述:

已知x=

5
+3,y=
5
-3,求下列各式的值:
(1)x2-2xy+y2
(2)x2-y2

(1)∵x=

5
+3,y=
5
-3,
∴x-y=6,
∴x2-2xy+y2=(x-y)2=62=36;
(2)∵x=
5
+3,y=
5
-3,
∴x+y=2
5
,x-y=6,
∴x2-y2=(x+y)(x-y)=2
5
×6=12
5