已知x²-xy=13,xy-y²=-5,分别求出式子x²-y²与x²-2xy+y²的值

已知x²-xy=13,xy-y²=-5,分别求出式子x²-y²与x²-2xy+y²的值
已知x²-xy=13,xy-y²=-5,分别求出式子x²-y²与x²-2xy+y²的值

已知x²-xy=13,xy-y²=-5,分别求出式子x²-y²与x²-2xy+y²的值
x²-xy=13 ①
xy-y²=-5 ②
①+②
得x²-y²=8
①-②
得x²-2xy+y²=18

x²-xy=13····a
xy-y²=-5·····b
a-b得：x²-2xy+y²=18
a+b得：x²+y²=8

已知x²-xy=13，xy-y²=-5，
x²-y²=x²-xy+(xy-y²)=13-5=8;
x²-2xy+y²=x²-xy-(xy-y²)=13-(-5)=18;