若X的平方减Y的平方减X加Y等于X减Y的差乘A,则A等于
问题描述：
若X的平方减Y的平方减X加Y等于X减Y的差乘A,则A等于
答
x^2-y^2-x+y=A(x-y)
由平方差公式得(x-y)(x+y)-(x-y)=A(x-y)
提取公因式得(x-y)(x-y+1)=A(x-y)
所以A=x-y+1
答
x^2-y^2-x+y=(x-y)A
(x-y)(x+y)-(x-y)=(x-y)A
(x-y)(x+y-1)=(x-y)A
(x-y)(x+y-1)-(x-y)A=0
(x-y)(x+y-1-A)=0
(x-y)=0或(x+y-1-A)=0
x=y或A=x+y-1
所以当x=y时,A为任意实数；或A=x+y-1