已知x=5+3,y=5-3,求下列各式的值; (1)x2-xy+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-xy+y2,
(2)x2-y2.
答
∵x=
+3,y=
5
-3,
5
∴x+y=2
,x-y=6,xy=5-9=-4,
5
∴(1)x2-xy+y2
=(x-y)2+xy
=62+(-4)
=32.
(2)x2-y2.
=(x+y)(x-y)
=2
×6
5
=12
.
5