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=

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

∵x=

5
+3,y=
5
-3,
∴x+y=2
5
,x-y=6,xy=5-9=-4,
∴(1)x2-xy+y2
=(x-y)2+xy
=62+(-4)
=32.
(2)x2-y2
=(x+y)(x-y)
=2
5
×6
=12
5