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=
+3,y=
5
-3,求下列各式的值:
5
(1)x2-2xy+y2
(2)x2-y2.
答
(1)∵x=
+3,y=
5
-3,
5
∴x-y=6,
∴x2-2xy+y2=(x-y)2=62=36;
(2)∵x=
+3,y=
5
-3,
5
∴x+y=2
,x-y=6,
5
∴x2-y2=(x+y)(x-y)=2
×6=12
5
.
5