x3-y3-3xy=1 x-y=?

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x3-y3-3xy=1x-y=?x3-y3-3xy=1x-y=?x3-y3-3xy=1x-y=?(x-y)^3=x³-3x²y+3xy²-y³则x3-y3-3x

x3-y3-3xy=1 x-y=?
x3-y3-3xy=1 x-y=?

x3-y3-3xy=1 x-y=?
(x-y)^3=x³-3x²y+3xy²-y³ 则
x3-y3-3xy=1
(x-y)^3+3x²y-3xy²=1
(x-y)^3+3xy(x-y)=1
(x-y)((x-y)2+3xy)=1

解不出,差一个条件。

解,X^3-y^3-3XY-1=(x-y)(x^2+xy+y^2)-3xy-1=0,令x-y=a,故上式等于a(a^2+3xy)-3xy-1=a^3-1+3xy(a-1)=(a-1)(a^2+a+1+3xy)=0,因为x^3-y^3-3xy大于0所以x大于y,故,后式不等于0.所以a=1,所以x-y=1