∵x²-xy=40
∴x²=40+xy......................................①
∵xy-y²=10
∴y²=xy+10......................................②
∵x²-y² =①-②
∴原式:x²-y²=40+xy-xy-10=30
又∵①+②为:
x²+y²=50+2xy
∴x²-2xy+y²=50
【这样比较好理解】
x²-xy=40 ①
xy-y²=10 ②
由①+②得x²-y²=50
由①-②得x²-2xy+y² =30
x²-y²=(x²-xy)+(xy-y²)=50
x²-2xy+y² =(x²-xy)-(xy-y²)=10
望采纳
第一个x(x-y)=40 ;
第二个y(x-y)=10 ;
一二相加则是(x-y)(x+y)=x²-y² =50
一二相减则是x²-2xy+y² =30
x(x-y)=40
y(x-y)=10
两式相加(x+y)(x-y)=x²-y²=50
两式相减(x-y)(x-y)=x²-2xy+y²=30