已知x+y=6,xy=8,则x2+y2=_,(x-y)2=_.

问题描述:

已知x+y=6,xy=8,则x2+y2=______,(x-y)2=______.

∵x+y=6,
∴x2+2xy+y2=36,
∵xy=8,
∴x2+y2=36-2×8=20;
∴(x-y)2=x2-2xy+y2=20-2×8=4.
故答案为:x2+y2=20,(x-y)2=4.