已知x^3=10-y^3,x^2y-xy^2=-3,求代数式(x^3-y^3)-(2x^y-4xy^2)-2(-y^3+xy^2)的值
问题描述:
已知x^3=10-y^3,x^2y-xy^2=-3,求代数式(x^3-y^3)-(2x^y-4xy^2)-2(-y^3+xy^2)的值
答
x^3=10-y^3,x^2y-xy^2=-3
则x^3+y^3=10,x^2y-xy^2=-3
(x^3-y^3)-(2x^y-4xy^2)-2(-y^3+xy^2)
=x^3-y^3-2x^y+4xy^2+2y^3-2xy^2
=x^3+y^3-2x^y+2xy^2
=(x^3+y^3)-2(x^y-xy^2)
=10+6
=16