用反证法证明:已知x,y属于R,且x^3+y^3=2,则x+y=

问题描述:

用反证法证明:已知x,y属于R,且x^3+y^3=2,则x+y=

设:x+y>2
则:x^3+y^3=(x+y)(x^2+y^2-xy)
>2[(x+y)^2-3xy]
>2(4-3xy)
≥2(4-3*(x+y)^2/4)
>2(4-3*4/4)
=2(4-3)
=2
即:x^3+y^3>2
与x^3+y^3=2矛盾
所以
x+y=