given that x^3-y^3=(x-y)^3 and that x-y=d (where d not equal to 0),show that 3xy=d^3-d^2.

given that x^3-y^3=(x-y)^3 and that x-y=d (where d not equal to 0),show that 3xy=d^3-d^2.

题目

given that x^3-y^3=(x-y)^3 and that x-y=d (where d not equal to 0),show that 3xy=d^3-d^2.

答案

x^3-y^3=(x-y)*(x^2+y^2+xy)=(x-y)^3,x^2+y^2+xy=(x-y)^2=d^2,(x+y)^2-2xy+xy=(x+y)^2-xy,d^3-xy=d^2,所以xy=d^3-d^2.

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