当x与y为实数,且x+y=1时,说明x·x·x+y·y·y-xy的值是非负数x^3 + y^3 -xy
问题描述：
当x与y为实数,且x+y=1时,说明x·x·x+y·y·y-xy的值是非负数
x^3 + y^3 -xy
答
x^3 + y^3 -xy
=(x+y)(x^2-xy+y^2)-xy
=x^2-2xy+y^2
=(x-y)^2
=(2x-1)^2>0
非负
答
x^3 + y^3 -xy
=(x+y)(x^2-xy+y^2)-xy
=x^2-2xy+y^2
=(x-y)^2 》0
答
x+y=1===>y=1-x.故x^3+y^3-xy=(1-x)^3+x^3-x(1-x)=1-3x+3x^2-x^3+x^3-x+x^2=4x^2-4x+1=(2x-1)^2》0.故原命题真.
答
x^3 + y^3 -xy
=(x+y)(x^2-xy+y^2)-xy
=x^2-2xy+y^2
=(x-y)^2 非负