若x

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/17 22:05:47

若x

(x^2+y^2)(x-y)-(x^2-y^2)(x+y)
=(x^2+y^2)(x-y)(x-y)(x+y)^2
=(x-y)[(x^2+y^2)-(x+y)^2]
=(x-y)(x^2+y^2-x^2-y^2-2xy)
=-2xy(x-y)
由x0 x-y<0
又-2<0
因此(x^2+y^2)(x-y)-(x^2-y^2)(x+y)>0
(x^2+y^2)(x-y)>(x^2-y^2)(x+y)